We present a computational method for adequate and efficient coupling of the multigroup neutron transport equation with the precursor and heat transfer equations. It is based on the multilevel nonlinear quasi-diffusion (QD) method for solving the multigroup transport equation. The system of equations includes the time-dependent high-order transport equation and time-dependent multigroup and effective one-group low-order QD equations. We also apply the α-approximation for the time-dependent high-order transport equation. This approach enables one to avoid storing the angular flux from the previous time step. Numerical results for model transient problems are presented.