In a report on model evaluation, the authors ran the HYDRUS Code, among other transport codes, to evaluate the impacts of nonequilibrium sorption sites on the time-evolution of (sup 99)Tc and (sup 90)Sr through the vadose zone. Since the authors' evaluation was based on a rather low, annual recharge rate, many of the numerical results derived from HYDRUS indicated that the nonequilibrium sorption sites, in essence, acted as equilibrium sorption sites. To help explain these results, the authors considered a 'stripped-down' version of the HYDRUS system. This 'stripped-down' version possesses two dependent variables, one for the radionuclides in solution and the other for the radionuclides adsorbed to the nonequilibrium sites; and it possesses constant physical parameters. The resultant governing equation for the radionuclides in solution is a linear, advection-dispersion-reaction (i.e., radioactive decay) partial differential equation containing a history integral term accounting for the nonequalibrium sorption sites. It is this 'stripped-down' version, which is the subject of this paper.