This study is concerned with two-group reactor kinetics in a multi region reactor for problems which involve time-dependent coefficients and nonlinear terms. The method of solution described can be used in problems in which the cross sections are given as linear combinations of powers of the fluxes or as powers of the integrated fluxes. Numerical integration schemes are suggested to solve this class of problems. Included in the possible inherent shutdown mechanisms of a reactor is the Doppler broadening of absorption resonances. It is this particular phenomenon that is used in a Model Problem to illustrate techniques that may be used to solve a much wider class of problems. The Model Problem is based on two-group diffusion theory, with one group of delayed neutrons, in a multi region slab reactor. The results obtained are readily extensible to cylindrical and spherical geometries in one space variable.