With the increasing pressure on natural resources, the sustainability study of socio-ecological systems has become a crucial scientific issue. In this paper we emphasize that transient behaviors have to be taken into account in sustainability analysis. We illustrate their impact with a model of tourism development from the literature, where the sustainability study is based on asymptotic properties. In order to evaluate relevant space and time characteristics of transient dynamics, we propose to use the concepts and tools of the mathematical viability theory. We also extend this analysis to controlled dynamical systems, which are particularly appropriate to model socio-ecological systems when management issues are at stake.