Abstract. An integer-valued analogue of the classical generalized autoregressive conditional heteroskedastic (GARCH) (p,q) model with Poisson deviates is proposed and a condition for the existence of such a process is given. For the case p = 1, q = 1, it is explicitly shown that an integer-valued GARCH process is a standard autoregressive moving average (1, 1) process. The problem of maximum likelihood estimation of parameters is treated. An application of the model to a real time series with a numerical example is given.