The presence of transient animals, common enough in natural populations, invalidates the estimation of survival by traditional capture- recapture (CR) models designed for the study of residents only. Also, the study of transit is interesting in itself. We thus develop here a class of CR models to describe the presence of transients. In order to assess the merits of this approach we examme the bias of the traditional survival estimators in the presence of transients in relation to the power of different tests for detecting transients. We also compare the relative efficiency of an ad hoc approach to dealing with transients that leaves out the first observation of each animal. We then study a real example using lazuli bunting (Passerina amoena) and, in conclusion, discuss the design of an experiment aiming at the estimation of transience. In practice, the presence of transients is easily detected whenever the risk of bias is high. The ad hoc approach, which yields unbiased estimates for residents only, is satisfactory in a time-dependent context but poorly efficient when parameters are constant. The example shows that intermediate situations between strict 'residence' and strict 'transience' may exist in certain studies. Yet, most of the time, if the study design takes into account the expected length of stay of a transient, it should be possible to efficiently separate the two categories of animals.