A finite cellular automaton (CA) forms cycles in its configuration space. The configurations, which are part of a cycle, are called cyclic configurations and the rest are acyclic configurations. In a reversible (finite) CA, all the configurations are cyclic. Whereas, an irreversible (finite) CA contains both the cyclic and acyclic configurations. This chapter deals with linear and complemented cellular automata (CAs) and characterizes the cycles formed by them.