Stochastic dynamic programming techniques are used to formulate and solve the problem of tracking two independent and stationary targets with one sensor in order to maximize a certain measure of performance. At any point in time, the sensor, usually a passive sonar array, can be allocated to only one of the two targets. Assuming the fluctuation process in the ocean to be governed by a phase‐random multipath law, the sensor ’’holds’’ the target when ρ, the root‐mean‐square pressure at the receiver, is above a user‐specified threshold. Using discrete time models for the ocean acoustic detection process formulated in earlier papers, we solve the problem for a finite horizon of observations using several alternative objective and reward/penalty functions. Delays of user‐specified magnitude in ’’switching’’ from one target to the other are also incorporated in our algorithms. Examples using both real and simulated data are presented and discussed. Finally, future research directions are suggested.