Abstract: Based on the EM algorithm and Laplace approximation, this paper presents a method of influence analysis for zero inflated longitudinal count data models. To detect the influential observations in clustered count data with excess zeros, we regard the random effects as the missing data and put certain weight to the data with zero values in ZI longitudinal data models. According to this fact, we develop the influence method for the model based on the conditional expectation of the complete-data log-likelihood function and the associated Q-distance function under the EM algorithm. The Laplace approximation is also employed for integral computing in E-step. Then the case-deletion model and the local influence analysis are investigated for the model and several diagnostic measures are obtained. Finally, a numerical example of the real count data is given to illustrate the results in this paper.