A Dynamic Programming formulation is used to obtain an optimal strategy for the handoff problem in cellular radio systems. The formulation includes the modeling of the underlying randomness in received signal strengths as well as the movements of the mobile. The cost function is designed such that there is a cost associated with switching and a reward for improving the quality of the call. The optimum decision is characterized by a threshold on the difference between the measured power that the mobile receives from the base stations. Also we study the problem of choosing the ﲢest fixed threshold that minimizes the cost function. The performance of the optimal and suboptimal strategies are compared.