Credible equilibria were defined in Ferreira et al. [6] to handle situations of preferences changing along time in a model given by an extensive form game. This paper extends the definition to the case of infinite games and, more important, to games with non-perfect recall. These games are of great interest in possible applications of the model, but the original definition was not applicable to them. The difficulties of this extension are solved by using some ideas in the literature of abstract systems and by proposing new ones that may prove useful in more general settings.