The purpose of this paper is to study certain categorical properties of the categories SoftAct of all soft S-acts and soft homomorphisms, and WSoftAct of all soft S-acts and weak soft homomorphisms. We investigate the interrelations of some particular morphisms, limits and colimits in SoftAct and WSoftAct with their corresponding notions in the categories ActS and Set. It is proved that SoftAct has non-empty soft coproducts and soft coequalizers and then soft pushouts. Moreover, WSoftAct has arbitrary w-soft products and non-empty w-soft coproducts. Some results concerning soft equalizers and w-soft pullbacks are also presented.