A technique is exhibited which permits an investigation of the changes in flux shape which occur when reactivity is inserted locally in an inhomogeneous reactor system and the power level rises. Thus, transient flux shapes at any time may be found as well as the asymptotic flux shape which is eventually attained. The reactor kinetics study in this article is motivated by a method of harmonics which does not employ the conventional assumption of separability of the flux into a product of a function of position alone and a function of time alone. From the point of view of practical applications the method is restricted to systems of rather simple geometry in which the slowing down is everywhere uniform and in which there are no nonlinear feedback effects.