Recent theoretical works on the dynamics of metapopulations have highlighted the existence of very long transients (supertransients) with abrupt changes in behaviour which occur following perturbation of the system away from its attractor. If this phenomenon is common in natural systems, populations that do not oscillate can begin to fluctuate wildly without any change in the environmental conditions. However, the frequency of occurrence of supertransients is currently poorly understood even in model systems. Here we explore their occurrence in metapopulation models which relax the important assumption of global synchrony of events implicit in all the coupled map lattice models for which supertransients have so far been demonstrated. We find supertransients in all the models but always only for a very restricted range of parameter combinations. However, we also report for the first time another type of longer-lived transient (mesotransients) that occurs on shorter time-scales than supertransients and is found for a much wider set of conditions. We argue that these medium-term changes in the dynamics of populations can be of more ecological relevance than the long-term changes of supertransients.