This paper develops the asymptotic theory for the estimation of smooth semiparametric generalized estimating equations models with weakly dependent data. The paper proposes new estimation methods based on smoothed two-step versions of the Generalized Method of Moments and Generalized Empirical Likelihood methods. An important aspect of the paper is that it allows the first step estimation to have an effect on the asymptotic variances of the second-step estimators and explicitly characterizes

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... s effect for the empirically relevant case of the so-called generated regressors. The results of the paper are illustrated with a partially linear model that has not been previously considered in the literature. The proofs of the results utilize a new uniform strong law of large numbers and a new central limit theorem for U -statistics with varying kernels that are of independent interest.