The multigroup neutron kinetics equations are derived and investigated for the case when the within-group weighting spectra, which are used in defining group constants, are space- and time-dependent. New terms are introduced by the space- and time-dependence of these weighting spectra. The derivation is carried through the hierarchy of operations by which the continuous space, time, and lethargy dependence is replaced by a discrete representation. The new terms do not alter the usual positivity properties associated with the discrete multigroup kinetics equations, provided that certain conditions are satisfied. Conditions are also established which are sufficient to ensure that the discrete representation is adjoint consistent; i.e., the discrete representation of the adjoint equation is mathematically adjoint to the discrete representation of the direct equation. A similar development is presented for the Spectral Synthesis approximation. Conditions are established for the adjoint consistency of the discrete representation. The type of positivity argument made for the multigroup equations is shown to be invalid for the Spectral Synthesis equations.