Computer simulation of coagulation is the subject of this paper. Zero order approximate methods offer distinct advantages in many cases, combining satisfactory accuracy, simplicity, and efficiency of computation. Methods proposed by Batterham et al (in ''Proceedings, 3rd International Symposium on Agglomeration, Nurnberg, 1981,'' pp. A136-A150), Marchal et al (J. Chem. Eng. Sci. 43, 59 (1988)). Gelbard et al (J. Colloid Interface Sci. 76, 541 (1980)), and Hounslow et al (AlChE J. 34, 1821 (1988)) are systematically evaluated by comparison with analytical solutions. Two kernels (constant and sum) are employed with monodisperse and gamma initial distributions for short and long times. The performance characteristics of these methods (under various conditions) are outlined. Overall the method of Hounslow et al. exhibits the best performance, with the additional advantage of conserving both particle number and mass. The merits of the methods by Batterham et al. and Gelbard et al. are also presented. ''Numerical gelation'' phenomena obtained in some cases are identified. (C) Academic Press, Inc.