Multiple imputation (MI) is increasingly being used as a sophisticated tool to handle missing data in the recent years. The standard MI techniques use Bayesian sampling methods for making posterior draws for the imputations and analyse the imputed data sets under a frequentist framework. However, the software packages that are used to implement these techniques are not yet fully flexible to account for the non-normality of the incomplete variables in repeatedly measured data sets. Multiple imputation can be performed in a fully Bayesian modelling context, which offers a flexible alternative in terms of fitting hierarchical non-normal imputation models. This work is motivated by an observational cohort study which consists of different types of incomplete time-varying variables, such as skewed continuous, ordered and unordered categorical variables. These variables were imputed using hierarchical Bayesian imputation models, such as multivariate truncated normal, gamma, multinomial and logistic. The estimates of the analysis model obtained with fully Bayesian imputation method were compared to standard MI methods, which assume normality of the incomplete variables. In addition, the performance of the fully Bayesian imputation was evaluated with a simulation study, under different settings of incomplete data.