The purpose of this paper is to present the mechanics of the derivation of Avery's coupled reactor kinetics equations, which have been given by his physical consideration. Firstly, the diffusion equation and its adjoint equation are expressed in the matrix form. Then the partial flux and the partial adjoint flux are defined explicitly. The neutron flux, introduced by Henry, is represented as an amplitude T(t) times a shape function ψ(r, t). The adiabatic approximation is adopted in the neutron-flux shape function. Using the commutation law (given in the Appendix) between the diffusion operator and its adjoint operator, Avery's equations are derived from the time-dependent diffusion equations for the partial adjoint flux. The assumptions introduced are; (a) the delayed-neutron fission spectrum is the same as the prompt-neutron fission spectrum, (b) the neutron-flux shape function is approximated by the adiabatic method, (c) the time constant of the amplitude T(t) is much smaller than the minimum time constant of the shape function ψ(r, t) at that instant. As the result of these assumptions, the delay time associated with the transfer of neutron does not appear explicitly in Avery's equations.