This work deals with the asymptotic properties of maximum likelihood estimators for semi-Markov processes with parametric sojourn time distributions. It is motivated by the comparison, via a two-sample test procedure, of the distribution of two panels of qualitative trajectories modeled by semi-Markov processes and observed over a random number of transitions. Considering first one panel of growing size, we derive, under classical conditions, the convergence in probability of the estimators of the transition probabilities and the parameters of the sojourn time distributions as well as their asymptotic normality. We then consider panels of semi-Markov processes drawn from two different populations and study two-sample tests based on likelihood ratio. We also introduce a two-sample Wald type test. The finite sample performances of the proposed two-sample tests are evaluated with a brief simulation study.