We have investigated the effects of nonequilibrium ionization on magnetic loop models with a steady siphon flow that is driven by a nonuniform heating rate. In particular, we have considered the model developed by Mariska to explain the observed redshifts of transition region emission lines, and we have computed the number densities of the ions of carbon and oxygen along the loop, with and without the approximation of ionization equilibrium. Considerable deviations from equilibrium have been found. In order to determine the consequences of these nonequilibrium effects on the characteristics of the EUV emission from the loop plasma, we calculated the profiles and wavelength positions of all the important emission lines due to carbon and oxygen. Our calculations are in broad agreement with the conclusions reached by Mariska, although they show a significant diminution of the Doppler shifts, as well as modifications to the line widths. We conclude that the inclusion of nonequilibrium effects makes it more difficult to reproduce the observed characteristics of the solar transition region by means of the asymmetric-heating models.