This paper sets up a formalism that is sufficiently general to describe the effects of photofission, photonuclear, (n, xn), (n, n'xγ), and (n, xγ) reactions on the neutron-gamma Feynman-alpha variance-to-mean ratios. Such a formalism is obtained using the Chapman-Kolmogorov (master) forward equation for the above-mentioned set of nuclear reactions. Thereafter, the issue of estimating reaction intensities for gammas in the master equation is highlighted by the paper. As an example, a quantitative evaluation of reaction intensities is given for a case when (n, γ), photonuclear, and (n, 2n) reactions are relevant for the system. However, an evaluation of the influence of these types of reactions to the values of the Feynman variance-to-mean ratios is not within the scope of this paper. Overall, the results obtained in this paper are intended to give an extended systematic framework for the study of the neutron- and gamma-based nondestructive assay problems in nuclear reactor applications and materials control.