In this thesis, we investigate semiparametric partially linear marginal models for binary and count longitudinal data with dropouts. Specifically, we focus on the joint estimation of the marginal mean, association and dispersion parameters through generalized second-order estimating equations where the marginal mean response model is partially linear. We discuss a series of weighted generalized estimating equations (GEEs) to fit regression models to binary and count longitudinal responses when dropouts occur. The proposed method offers efficient estimators of the model parameters under a specified missing data mechanism. Simulations are conducted to examine the robustness characteristics of the method suggested under both accurately defined and inaccurately stated correlation frameworks. The approach is also demonstrated us- ing some real missing longitudinal data on patterns of smoking, where the goal is to study the development of coronary arteries in young adults. A semiparametric approach for analyzing binary and longitudinal count data is also developed. We used the second-order GEE approach to examine longitudinal responses in partially linear models. Additionally, the smoothing technique is suggested for estimating the nonparametric part of the model based on a spline approximation. In simulations, the analytical properties of the proposed method are evaluated. The proposed estimator effectively takes into consideration the association within the subject/cluster and is easy to implement. Our simulation study shows that when the underlying model is partly linear, the proposed method offers unbiased and efficient estimators.Next, we propose a weighted regression spline second-order GEE approach for simultaneous estimation of the nonlinear function, regression, association and dispersion parameters in partially linear models with dropouts. As an application of the proposed semiparametric weighted GEE, we analyzed some longitudinal count data obtained from a health survey, referred to as the Health and Retirement study (HRS)(HRS, 2019), where the mean response function shows a nonlinear trend in terms of associated covariates. The results from the data analysis appear to be very encouraging. From this application it is evident that our proposed methods can be used to improve the efficiency of the estimates obtained from an ordinary GEE model for longitudinal binary and count data with dropouts.