This paper explores the problems of fitting antedependence (AD) models to continuous non-Gaussian longitudinal data. AD models impose certain conditional independence relations among the measurements within each subject. The models are parsimonious and useful for data exhibiting time dependent correlations. Since the relation of conditional independence among variables is rather restrictive, we consider AD multivariate skew normal models. The multivariate skew normal distribution not only shares some nice properties with multivariate normal distributions but also allows for any value of skewness. We derive necessary and sufficient conditions on the shape and covariance parameters for multivariate skew normal variables to be AD(p) for some p. Likelihood-based estimation as well as likelihood ratio hypothesis tests for the order of antedependence and for zero skewness under the models are presented. Numerical results show that the proposed models may provide reasonable fits to some continuous non-Gaussian longitudinal data set.