Article dans une revue: In this paper, we introduce a notion of continuous implementation and characterize when a social choice function is continuously implementable. More specifically, we say that a social choice function is continuously (partially) implementable if it is (partially) implementable for types in the model under study and it continues to be (partially) implementable for types "close" to this initial model. Our results show that this notion is tightly connected to full implementation in rationalizable strategies.