The mental processes involved in performing some tasks can be represented as directed arcs in an acyclic network. A path directed from the head of one arc to the tail of another indicates that the process represented by the first arc must be executed prior to the process represented by the second arc. If there is no directed path from one arc to another, the corresponding processes can be executed concurrently. Information about the arrangement of processes in an acyclic network can be found from the effects on response times of factors selectively influencing the processes. The methodology was developed earlier for critical path networks, in which a process begins execution when all its immediate predecessors have finished. This paper considers shortest path networks, in which a process begins execution as soon as any immediate predecessor is finished. Results analogous to those for critical path networks are reported. New results are presented enabling investigators to distinguish sequential and concurrent processes in both critical path and shortest path networks. This information is sufficient to construct an acyclic network representing the processes. Further, by examining the effects of selectively influencing processes, one can determine whether a task network is a critical path network or a shortest path network.