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Published September 6, 2026 · By Vincent KENNEL
Task dependencies: why there are four link types, not five
Four link types, two of them barely used, and lags that most explanations leave out entirely. What a link actually declares about the work, where the four came from, and why a lag means something different depending on the arrow that carries it.
In brief
A task dependency is a logical relationship between two activities, or between an activity and a milestone (PMI Lexicon of Project Management Terms, 2012). There are exactly four types, because a link joins one end of the predecessor to one end of the successor. A lag is the distance carried by that link, positive or negative.
On a contract programme, the question a steering committee asks is almost never when one task will finish. It is what a slip upstream does to a contractual milestone six months out. A list of dates cannot answer that, because a list of dates computes nothing: someone moves each one by hand, and that person decides what moves with it. A network answers it, because the answer is already declared inside it.
What a dependency network is
The logical relationship
The reference definition is short. A logical relationship is a dependency between two activities, or between an activity and a milestone (PMI Lexicon of Project Management Terms, 2012, carried over word for word into the PMBOK Guide, 6th edition, 2017). The schedule network diagram is the graphical representation of those relationships across the schedule activities.
Two things in that definition matter more than they look.
The first is that a dependency can join an activity and a milestone, not only two activities. On a contract schedule that half is the one that pays: contractual milestones are exactly what the rest of the network has to answer to.
The second is what the object actually is. The precedence diagramming method builds a schedule model in which activities are nodes, linked by one or more logical relationships that give the order in which they are to be performed (PMBOK Guide, 6th edition, 2017, §6.3.2.1). Dates are the output of that model, not its content. Change a duration and the network recomputes. Change a duration in a list of dates and nothing happens until a human works out what else has to move. That difference in kind is what pays for the effort of declaring anything at all.
Why there are four link types, and not five
The four types are usually presented as a table with one example per row, which asks you to memorise a list. The list is deducible, and deducing it once is worth more than remembering it four times.
A task has two ends, a start and a finish. A link leaves one end of the predecessor and arrives at one end of the successor. Two by two gives four combinations, and there is no fifth to look for. That is where finish-to-start (FS), start-to-start (SS), finish-to-finish (FF) and start-to-finish (SF) come from.
A link joins two task ends. Crossing them yields exactly four.
What the figure does not say is what each of the four declares about the work. Take a sequence you will recognise on any contract: a supplier fabricates and delivers a piece of equipment, a site team installs it, and an acceptance file is compiled for handover.
Finish-to-start: installation needs the finished product of fabrication. The successor needs what the predecessor produced.
Start-to-start: the acceptance file starts once installation has started. The successor works the same front, behind the predecessor.
Finish-to-finish: the acceptance file cannot be closed while installation is still producing what goes into it.
Start-to-finish: fabrication and delivery cannot finish until installation starts. It reads backwards, and it is meant to. The supplier's activities have no schedule logic of their own, the team wants the site dates to drive the delivery dates, and since a predecessor always drives its successor, making installation the predecessor is the only way to get that (PMI Practice Standard for Scheduling, 3rd edition, 2019).
The last one is the odd one out. The PMBOK Guide, 6th edition (2017) calls it very rarely used, and says it is included to present a complete list of the relationship types. The 1996 edition of the same guide was blunter, reserving it to professional scheduling engineers; that phrasing did not survive into the later editions.
The lag, a distance carried by the link
A lag is not a second object bolted onto a link. It is a distance carried by the arrow itself.
The reference pair is symmetric. A lag is the amount of time by which a successor activity is required to be delayed with respect to its predecessor, and a lead the amount by which it can be advanced (PMI Lexicon of Project Management Terms, 2012). The PMBOK Guide, 6th edition (2017) adds the practical note that scheduling tools usually encode a lead as a negative lag.
Here is the part that makes links and lags one system rather than two chapters. The same "+2" does not say the same thing depending on which arrow carries it. On a finish-to-start, it means two days after the predecessor finishes. On a start-to-start, two days after the predecessor starts. You are not picking a type and then adding a lag to it: you are declaring a distance between two designated ends.
The same lag, two anchor points, two schedules.
Two days counted on which calendar? One source in the reference literature answers, and it answers plainly: a lag is an offset from an activity to its successor, based on the calendar of the predecessor activity (AACE International Recommended Practice 29R-03, revision of 25 April 2011, §4.3.D).
A negative distance is an overlap. There is more than one way to declare one.
What the network buys you on a contract project
Three rules follow, and all three are usable on the next schedule you open.
Interfaces are declared as links, not as dates. The Delay and Disruption Protocol, 2nd edition (2017), published by the Society of Construction Law, is explicit at guidance §1.41 to 1.51: the employer's interfaces should be modelled by logically linking to the contractor's activities, and not by means of fixed dates. Every necessary link should be inserted, excessive leads and lags avoided, and what remains justified in the programme narrative. On a contract, a dependency is not only a sequencing decision, it is an interface between parties.
Finish-to-start is the default, and the rest earns its place. The majority of relationships within a detailed schedule should be finish-to-start (GAO Schedule Assessment Guide, GAO-16-89G, 2015). The PMI Practice Standard for Scheduling, 3rd edition (2019), gives the reason: finish-to-start relationships produce the simplest and least complicated calculations for the schedule model. That is not a ban on the other three. It is a burden of proof on whoever uses them.
Work does not hide inside a lag. Lags use no resources (GAO-16-89G, 2015). Where a lag would stand in for effort, the PMI Practice Standard for Scheduling, 3rd edition (2019), asks for that work to be shown as an activity in the schedule model instead. The test comes as a pair and it takes ten seconds: twenty-one days of concrete curing is a legitimate lag, because nobody is working; six weeks of fabrication at a supplier is not a lag, it is a task. Francis and Miresco (2012) draw the same line, separating a lag of technical nature from one that is covering a workload.
A link is not a date constraint. A pinned date immobilises the task it sits on: the network stops recomputing around it, and a slip upstream stops showing up downstream. A link declares a relationship, a constraint declares a date. It is the same distinction the Delay and Disruption Protocol, 2nd edition (2017), makes when it asks for interfaces to be linked logically rather than fixed by date.
Where it comes from
Four dated moments, three of them first-hand.
1959, and the founding model knows one link. In the paper that introduced critical path planning, it is tacitly assumed that each job in a project is defined so that it is fully completed before any of its successors can begin (Kelley and Walker, Critical-Path Planning and Scheduling, proceedings of the Eastern Joint Computer Conference, Boston, 1 to 3 December 1959). Finish-to-start, zero lag, nothing else. The other three types and the lags all come later. With no lag mechanism in the model, a delivery restraint there is a job, an activity in its own right.
1958 to 1961, the node against the arrow. John W. Fondahl was working under a Bureau of Yards and Docks contract for the U.S. Navy, three years from 1 July 1958. His model came out of industrial engineering flow charts rather than operations research: in a flow chart, an operation is represented by a circle. He came across CPM in June 1959 through a Business Week article, and chose not to move to the arrow for one reason he gives himself, the arrow diagram requiring frequent artificial devices called dummies to achieve proper logic, which seemed an unnecessary complication (Fondahl, Precedence Diagramming Methods: Origins and Early Development, Project Management Journal, vol. XVIII, June 1987).
1964, and the name comes from elsewhere. Still on Fondahl's account, an IBM announcement in early 1964 for the Project Control System on the 1440, work started in 1962 with H. B. Zachry Co., carried the label. He adopted "precedence diagramming" because with IBM using it, the label would probably prevail. Moder, Phillips and Davis, 3rd edition (1983), report the same sequence.
And the inventor's own second thoughts. By 1987 Fondahl wrote that computer applications of precedence diagramming were using lag factor relationships to such an extent that logic errors sometimes developed, and that lag factors had destroyed the simplicity of the method. He described himself as remaining a purist, an advocate of node diagramming, or of precedence diagramming only where there is very careful and limited use of lag factors. That is a dated statement by a named person, not a position taken here.
In France, at the same time. Bernard Roy developed a distinct node-based approach from a building construction scheduling problem in 1958, simultaneously and independently according to his biographers (Bouyssou and Vanderpooten, Bernard Roy, in Profiles in Operations Research: Pioneers and Innovators, Springer, 2011).
In short
Open your own schedule tomorrow and go through it link by link. Three questions for each one, and this article has equipped all three. Which two ends does it join? What does it declare about the work? Does its lag hide work that should be a task? A link you cannot answer for is a link to remove, or to replace with a task.
Stop guessing. See the real impact.
Frequently asked questions
Q.Should you ever use a start-to-finish link?
A correct schedule can be built without it. The sequences used to justify it can usually be rewritten in plain finish-to-start logic, by subdividing activities or finding better predecessors (GAO-16-89G, 2015). Its practical value is recognising one when it turns up in a schedule someone hands you.
Q.Is a negative lag the same thing as an overlap?
No. The overlap is the situation; a negative duration on the link is one way to declare it (AFITEP, Dictionnaire de management de projet, 3rd edition, 1996). There is another: the same result comes from a start-to-start link (Moder, Phillips and Davis, 3rd edition, 1983).
Q.Do the links determine the critical path?
Yes. The critical path is computed on the network, so the logic you declare is what it is computed from. How that calculation works, and what a float is, belong to their own article.
