This paper focuses on the important issue of strategies for tracking users in a mobile communication network. Since the users are mobile, the network must keep track of where the users are, a prerequisite for routing calls to the users. We assume, the mobile users periodically inform the network of its present location. Now, it is very important to decide an efficient location updation strategy, that will optimize the overhead in terms of usage of radio spectrum, and power, as well as the search cost for a mobile when a call is to set up. Static location updation strategies often result poor performance.Three dynamic location updation strategies have been considered here, namely, the time-based strategy, the movement-based strategy and the distance-based strategy. A memoryless movement pattern on a two-dimensional mesh topology of cells has been studied. Analytical models have been developed to compare the performances of the strategies. Simulation studies also have been made for performance evaluation.