The classes of sequences generated by time- and space- restricted multiple counter machines are compared to the corresponding classes generated by similarly restricted multiple tape Turing machines. Special emphasis is placed on the class of sequences generable by machines which operate in real time. Real-time Turing machines are shown to be strictly more powerful than real-time counter machines. A number of questions which remain open for real-time Turing machines are settled for real-time counter machines. © 1970 Academic Press, Inc.