Summary: A general procedure for solving the boundary-value problem of the unsteady multigroup coupled neutron diffusion and precursor equations is developed analytically for a multiregional nuclear reactor whose subregions are of arbitrary shapes and with arbitrary space-time dependent neutron multiplication properties. The method which is based on the formulation and application of composite region integral transforms is seen to accept various orders of analytical approximations that originate from the transformed space. The formalism does not cover circulating fuel precursors.