Abstract An exact formalism is derived for two-nucleon overlap functions. It is a straightforward generalization of the approach used earlier in studies of one-nucleon transfer. The extended basis shell model and the RPA generalization of this model are shown to follow naturally as approximations. Although these models are restricted to cases in which one of the nuclear states is a closed shell, the formalism presented is more general. It can be applied to nuclei away from closed shells. A sample calculation of the 42Ca- 44Ca overlap is presented to demonstrate the feasibility of the method. The methods are contrasted to those recently proposed by Meyer, Gerace and Walker. We argue that the method introduced by these authors for including hole-state contributions does not properly account for the Pauli principle.