We consider the following ordering for stochastic processes as introduced by Irle and Gani (2001). A process (Y t )t is said to be slower in level crossing than a process (Z t )t if it takes (Y t )t stochastically longer than (Z t )t to exceed any given level. In Irle and Gani (2001), this ordering was investigated for Markov chains in discrete time. Here these results are carried over to semi-Markov processes with particular attention to birth-and-death processes and also to Wiener processes.