The framework for a unified theory of nuclear structure is described in which the wave functions for different nuclear models are obtained by transformations on the actual nuclear wave function. This formulation provides a basis for explaining the success of weak-coupling models of the nucleus and showing that they are not in conflict with the assumption that nucleons have very strong mutual interactions. The explanation lies in the fact that only in certain circumstances can the "particles" in a nuclear model be interpreted as nucleons.We investigate the properties which transformation operators must have to change the nuclear wave function into a model wave function and consider how far these properties are satisfied in practice. Self-consistent equations are set up for a model having a product wave function in the particle variables, and it is shown that these equations can be solved in an approximation relevant to the problem of nuclear saturation.