Formal study of aspect-oriented languages is difficult because current theoretical models provide a range of features that is too limited and rely on encodings using lower-level abstractions, which involve a cumbersome level of indirection. We present a calculus, based on Abadi and Cardelli�s object calculus, that explicitly models a base language and a variety of point cut description languages. This explicit modeling makes clear the aspect-oriented features of the calculus by removing the indirection of some existing models. We demonstrate the generality of our calculus by presenting models for AspectJ�s open classes and advice, and HyperJ�s compositions, and sketching a model for DemeterJ�s adaptive methods.