Abstract.A new class CVNH£ of cascade parallel fc-nets of shift registers (briefly fc-nets) is introduced. A characterization of the fc-nets by means of their sets of state sequences is given. In particular the periodicity problem of state sequences is studied. Two subclasses CVMn = 1,2, of CVAfTZ^ are distinguished. The main attention is devoted to the class CVN7Z~ whose elements can be described by the transition graphs. In the last section the other classes of parallel fc-nets are introduced.