The covariate dependence in a higher order Markov models is examined. First order Markov models with covariate dependence are discussed and are generalized for higher order. A simple alternative is also proposed. The estimation procedure is discussed for higher order with a number of covariates. The proposed model takes into account the past transitions. Transitions are fitted and are tested in order to examine their influence on the most recent transitions. Applications are illustrated using maternal morbidity during pregnancy. The binary outcome at each visit during pregnancy is observed for each subject and then the covariate dependent Markov models are fitted. The results indicate that the proposed model can be employed for analyzing repeated observations conveniently.