Three logic functions are introduced, two of which are functions in two-variables, named sequential logic product and sequential logic sum, while the third, depending on only one variable, is termed sequential logic negation. An algebraic theory is developed for logic processes where time plays an essential part; the connection is pointed out between sequential logic and the algebraic theory of multiple-state finite automata. This connection finally leads to new methods of analysis, as well as of synthesis, for finite automata operating according to given sequential equations; these methods offer certain advantages over standard procedures. Results obtained are likely to be useful in the theory of digital computers.