Here we present some limit theorems for a general class of generalized linear models describing time series of counts Y1,…,Yn. Following Zeger (Biometrika 75 (1988) 621–629), we suppose that the serial correlation depends on an unobservable latent process {et}. Assuming that the conditional distribution of Yt given et belongs to the exponential family, that Y1|e1,…,Yn|en are independent, and that the latent process satisfies a mixing condition, it is shown that the quasi-likelihood estimators of the regression coefficients are asymptotically normally distributed.