In order that chemically induced dynamic electron polarization (CIDEP) can provide a means to explore dynamics in arbitrary systems such as inclusion compounds or sequential chemical reactions, the Bloch equations are extended for use with a system exhibiting electron spin polarization (ESP). Since CIDEP depends on time and external magnetic field and in this paper is observed by time-resolved electron paramagnetic resonance spectroscopy (TREPR), an algorithm for the general calculation of EPR signals that display ESP is presented. In particular, processes inducing magnetization transfer between hyperfine (hf) states are described by means of a kinetic matrix that is incorporated into the Bloch relaxation matrix. The utilized approach takes into account the complete set of hyperfine states of all involved species and can be applied to such different phenomena as chemical exchange, electron transfer, and secondary radical generation that affect the time dependence of the observed signal. Solutions to the linear differential equations are found numerically. Hence, other than the normal restrictions on the Bloch equations, no additional approximations are assumed, rendering the algorithm more generally applicable than previous analytical treatments. Only chemical diffusion is not included. Specific examples are discussed. The TREPR spectra of p-benzoquinone are analyzed in terms of magnetization transfer. Excellent agreement between the experimental data and the computations using the numerical method is achieved. With rate constants depending on pH and solvent, chemical exchange between the neutral and/or anionic semiquinones is found present in the signals of the radicals generated by laser flash photolysis.