Summary: In biomedical studies, panel count data have been extensively investigated. Such data occur if study subjects are monitored or observed only at some discrete time points during observation periods. In addition, these data may be collected from multiple centers, and study subjects from the same center might be correlated. Limited literature exists for clustered panel count data. Ignoring such cluster effects could result in biased variance estimation. In this paper, two semiparametric additive mean models are proposed for clustered panel count data. The first model contains a common baseline function across all clusters, while the second model features cluster-specific baseline functions. Some estimation equations are derived to estimate the regression parameters of interest for the proposed two models. For the common baseline model, the baseline function is also estimated. Given some regularity conditions, the resulting estimators are shown to be consistent and asymptotically normal. Extensive simulation studies are carried out and indicate that the proposed approaches perform well in finite samples. An application of the China Health and Nutrition Study is also provided for illustration.