The requirements for a theory of instruction can be described in the following list of criteria: 1) a model of the learning process; 2) specification of admissible instructional actions; 3) specification of instructional objectives; 4) a measurement scale that permits costs to be assigned to each of the instructional actions and payoffs to the achievement of instructional objectives. From these four elements it is possible to derive optimal instructional strategies. A theory of instruction is, in fact, a special case of what has come to be known in mathematical and engineering literature as optimal control theory. Precisely the same problems are posed in the area of instruction except that the system to be controlled is the human learner. To the extent that the above four criteria can be formulated explicitly, methods of the control theory can be used to derive optimal instructional strategies. Two examples involving the derivation of such strategies are considered in this paper: a computer-assisted instruction program for early reading and an individualized program for learning a foreign language vocabulary. Both are analyzed on control theoretic principles. (Author/MC)