The critical parameters of coupled fissionable assemblies in close proximity are studied by a variational technique based upon an integral equation for neutron conservation. Both diffusion and transport kernels can be used, and though the former is simpler, it may lead to considerable error in certain cases. An iterative method is used to solve the resulting integral equation for the case of identical spheres. The rapid convergence implies that a constant trial function for the flux is satisfactory. It is found that limiting values are rapidly approached as the separation increases and that the effect is more pronounced if the assemblies are in a vacuum than if they are embedded in matter.