There are two methods for applying path delay tests to a sequential circuit. We show that all path delay faults that can affect the rated-clock operation of the circuit are testable by the variable-clock method. Also, all path delay faults that are untestable by the variable-clock method are, in fact, untestable by the rated-clock method. However, some faults tested by the variable-clock method may be incapable of affecting the rated-clock operation. Our study is based on a finite-state machine model in which fault-free transitions are shown by green arcs. Faulty transitions are shown by red arcs. A test traverses successive arcs until a faulty output occurs. A variable-clock test can exercise more flexibility in selecting from green and red arcs. It can cover all functional paths, but may find only a proper subset of untestable paths. Our analysis assumes a delay fault, consisting of either a singly-testable path or multiply- testable paths, and hence corresponds to non-robust detection.