Approximate counting is an algorithm proposed by R. Morris which makes it possible to keep approximate counts of large numbers in small counters. The algorithm is useful for gathering statistics of a large number of events as well as for applications related to data compression (Todd et al.). We provide here a complete analysis of approximate counting which establishes good convergence properties of the algorithm and allows to quantify precisely complexity-accuracy tradeoffs. Introduction. As shown by an easy information-theoretic argument, maintaining a counter whose values may range in the interval 1 to M essentially necessitates log,M bits. This lower bound is of course achieved by a 1 standard binary counter. R. Morris [8] has proposed a probabilistic algorithm that maintains an