In this paper we indicate briefly how the methods of the algebraic solution of Markov chains with constant transition probabilities apply to the analysis of sequential machines. Mealy's model of a sequential machine is assumed. A stochastic matrix is associated with each such machine to provide a starting point for the analysis. ``Closed'' sets of states are then characterized, for example, by the appropriate theorems about Markov chains. A technique is formulated for reducing the connection matrix of any sequential machine to a canonical form.