A space-time kinetic theory is proposed based on the recognition of a much shorter neutron spectral relaxation time than the spatial relaxation time. The neutron flux is factorized into a slowly varying energy-space-time-dependent spectral-shape function ψ(E, r, t) and a fast varying space-time-dependent local amplitude function A(r, t). The energy-independent self-adjoint diffusion equation that determines the local amplitude A(r, t) is defined as the space-time kinetic equation. This space-time kinetic equation is then solved by further decomposing A(r, t) into a relatively slowly varying space-time-dependent spatial-shape function R(r, t) and a fast varying time-dependent point amplitude T(t), which satisfies the point kinetic equation. The functions T(t), R(r, t), and ψ(E, r, t) are iteratively successively calculated, each one with a time increment step of a different order of magnitude. The fast varying delayed-neutron-precursor distribution functions are calculated together with T(t), however without complicating the point kinetic equation. Compared to the conventional approach, this proposed theory makes use less frequently of the multigroup diffusion equation, but more frequently the self-adjoint space-time kinetic equation. In this formulation, the instantaneous flux, not the adjoint flux, is the natural weighting function. This makes the space-time kinetic parameters deducible from monitored neutron spatial distribution data, and therefore the formulation a more appropriate basis for an inverse kinetic theory.