Introduction: Seldom does the actual arrangement of control elements in a nuclear reactor confers to the ideal and convenient mathematical array. In order to achieve shim control. safety and regulation, it is desirable to design with rods of different sizes and materials. With given fuel element arrangement, typically in square or hexagonal lattice spacing, there will be rods located at different distances form the center of the core and from each other. As the reactor operates, absorbers will be withdrawn, leaving further asymmetries in the location of those remaining. It is the purpose of this report to develop in detail a two-group diffusion theory with as complete generality as possible. The method is as yet restricted to the unreflected core, or to the reflected core by use of reflector savings and bare equivalent geometries.