This paper adapts Hamiltonian Monte Carlo methods for application in log-symmetric autoregressive conditional duration models. These recent models are based on a class of log-symmetric distributions. In this class, it is possible to model both median and skewness of the duration time distribution. We use the Bayesian approach to estimate the model parameters of some log-symmetric autoregressive conditional duration models and evaluate their performance using a Monte Carlo simulation study. The usefulness of the estimation methodology is demonstrated by analyzing a high frequency financial data set from the German DAX of 2016.