An approximation method is proposed for calculating the detailed kinetic response of a reactor during a transient in which the space and time behaviors of the neutron flux are not separable. In order to test the validity of the method a particular transient is studied for a series of cores chosen so that the space-time behavior of the neutrons is nonseparable in varying degrees. A particularly simplified mathematical description of the neutrons allows an exact solution to be obtained and hence affords a means of verifying predictions of the approximation scheme. Agreement between exact and approximate calculations is encouragingly good.