A mixed mode sequential machine (MSM) is defined as a representation in which both synchronous (clocked) and asynchronous (unclocked) state transitions are allowed. The intent of the representation is to allow designers to consider both types of transitions in a single structure, thereby promoting the use of LSI devices such as ROM's or PLA's to resolve the realization question. The approach is thus different from conventional design methods, in which asynchronous problems are treated separately with separate devices. The problems of state reduction, state assignment, and realization are covered. Of particular note is the development of a ROM implementation, which allows both clocked and unclocked transitions to occur.