An investigation of the dynamical neutronics of such a system is the main purpose of this paper. For the sake of simplicity of the analysis, we shall focus our attention on neutrons of only one speed (as in) and on individual cosinusoidal time-modulation of the two opposing neutron beams, and on possible relative time advance between them. The rest of this paper is organized as follows. The next section contains the details of a one-dimensional setup formulation of the posing dynamical boundary value problem (BVP) for the modulated and timeadvanced right neutron beam source, which is appropriately mapped in space and time. The section that follows addresses the solution to the BVP for this right neutron beam in the usual space-time domain with an analysis of its dissipative and periodic "dispersive" components. The neutron density distribution due to the two opposing beams, in this (B/Gd) NCT setup, is reported in the fourth section. The utility and ballistic indices  tailored to this therapeutic setup are derived in the fifth section. Here also the therapeutic problem for a nonlinear optimization of these indices is formulated with the two modulation frequencies and relative time advance as control variables. The paper is concluded in the last section with some important remarks and suggestions for future relevant research.