As a generalization of the notion of a group coring in the sense of Caenepeel et al. [7], we introduce the notion of a lax group coring. Firstly, we provide a large class of examples of such a lax group coring by considering socalled lax group entwining structures and partial group entwining structures. Secondly, over a lax group entwining structure one can consider two different categories of modules M(ψ)CA and M(ψ)π−CA, which are in fact nothing else than categories of (group) comodules over the group coring one can associate to each lax group entwining structure. Finally, we study the category Aop]C∗Mπ of π-graded modules over the π-graded A-ring Aop]C∗, and show that it is isomorphic to the category M(ψ)π−CA. Moreover, if π is a finite group, then we have an equivalence of categories between Aop]C∗M and M(ψ)CA.