In order to test the control portion of communication software, specifications are usually fll"St abstracted to state machines, then test cases are generated from the resulting machines. The state machines obtained from the specification are often both partially-specified and nondeterministic, but no former work has been reported on test generation for such state machines. We come out with a method of generating test suites for the software that is modeled by partially-specified nondeterministic fmite state machines (PNFSM's). On the basis of intuitive notions, a conformance relation, called quasi-equivalence, is introduced for such machines, which serves as a guide to test generation. Our method is also applicable to completely-specified deterministic machines, partially-specified deterministic machines, and completely-specified nondeterministic machines, which are typical classes of PNFSM's. When applied to such classes of machines, this method yields not greater test suites with full fault coverage for each class of machines than the existing methods for the same class which also provide full fault coverage, when the number of states in implementation machines is bounded by a known integer. The test suites generated by the method can be used to check the conformance relation between a specification and its implementations.