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In this paper we examine the panel data estimation of dynamic models for count data that include correlated fixed effects and predetermined variables. Use of a linear feedback model is advocated, and its properties and estimation results are compared to those of a multiplicative distributed lag model. The standard Poisson conditional maximum likelihood estimator for non-dynamic models, which is shown to be the same as the Poisson maximum likelihood estimator in a model with individual specific constants, is inconsistent when regressors are predetermined. A quasi-differenced GMM estimator is consistent for the parameters in the dynamic model, but when series are highly persistent, there is a problem of weak instrument bias. An estimator is proposed that utilises pre-sample information of the dependent count variable,which is shown in Monte Carlo simulations to possess desirable small sample properties. The models and estimators are applied to data on US patents and R&D expenditure.