In this paper we introduce the category G-pAct of partial actions of a fixed group G.The objects or G-psets are the sets X endowed with a partial action of G on X and the morphisms, or preferably G-pmorphisms, are the maps preserving this action.As a special achievement, we extend several well-known constructions in the category G-Act, of global actions of G, to this new context.In particular, we characterize products, coproducts, equalizers and pullbacks for arbitrary G-pmorphisms.We also characterize coequalizers and pushouts for strong G-pmorphisms (category G-fpAct).Last, we prove that the category G-pAct is complete and the category G-fpAct is cocomplete.