For any pair of categories $$(\mathsf {C,K})$$ ( C , K ) enriched over the category $$\mathsf {Gpd}$$ Gpd of groupoids, it is possible to define a strong shape category $$SSh(\mathsf {C,K})$$ S S h ( C , K ) in such a way that, for $$\mathsf {C}$$ C the category of topological spaces and $$\mathsf {K}$$ K its full subcategory of spaces having the homotopy type of absolute neighborhoods retracts for metric spaces, one obtains the strong shape category $$SSh(\mathsf {Top})$$ S S h ( Top ) , as defined by Mardešić. We also introduce a new category $$SS_{\tiny \mathsf K}$$ S S K with the same objects as $$\mathsf {C}$$ C and morphisms given by suitable pseudo-natural transformations into the category of groupoids. The main result is then that such a category $$SS_{\tiny \tiny \mathsf K}$$ S S K is isomorphic to the strong shape category $$SSh(\mathsf {C,K})$$ S S h ( C , K ) , when $$\mathsf {C}$$ C is also a proper model category.