Here we propose a general class of generalized linear models to describe time series of counts Y₁, ... ,Y_n. Following Zeger (1988), we suppose that the serial correlation depends on an unobservable latent process . Assuming only that the conditional distribution of Y_t given belongs to the exponential family and that are independent, quasi-likelihood estimators of the regression coefficients are obtained. If, in addition, the latent process satisfies a mixing condition, then it can be shown that these estimators are asymptotically normal. The proof depends on an asymptotic result of Davidson (1992) for triangular arrays of weakly mixing random variables.