The rules for inheritance of classes with respect to data and function members are well defined. For example, the proposals for programming by contract in Eiffel ensure additional consistency between superclasses and subclasses. In object-oriented design, it is common to capture the behavior of classes with lifecycles, which are expressed in the form of finite state machines. In this context, there are very few proposals for what constitutes consistency between superclasses and subclasses.This paper presents proposals for consistency between superclasses and subclasses in the context of the Petri Net formalism, which is a form of finite state machine with explicit provisions for concurrency. The paper cites the applicability of these proposals in the context of network protocols, and argues for a similar applicability in the context of object lifecycles.