The aim of this project is to develop theoretical models that provide new understanding of the handoff problem in cellular communications networks. The performance of handoff algorithms in different propagation environments will be analyzed in terms of the tradeoff between unnecessary handoffs and handoff delay. Procedures for choosing parameters for existing algorithms will be developed. New optimal algorithms will be derived using the analytic models. Handoff algorithms will be analyzed using level crossing theory, an approach that has yielded promising preliminary results. Results from propagation analysis will be used to study the effect of radio channel characteristics on the handoff procedure. The design of optimal algorithms will involve the use of sequential decision making, and control and estimation theory. This project aims for fundamental theoretical results regarding the performance of handoff algorithms.