The microstructure and texture evolution in the Mg-2.9Y and Mg-2.9Zn solid solution alloys were investigated following rolling and subsequent isothermal annealing. The Mg-2.9Y alloy was hot rolled, and the Mg-2.9Zn alloy was rolled at room temperature in order to evaluate the possibility of attaining texture weakening by the suppression of dynamic recrystallization (DRX) and promotion of static recrystallization (SRX). It was found that texture weakening can be attained in Mg even in the absence of Y when there is no DRX, and SRX occurs during annealing. In solid solution, Y suppresses DRX during hot rolling, and retards the kinetics of SRX and grain coarsening in Mg. In the two alloys, the orientation of statically recrystallized grains at bands/twins (TSRX grains) is close to that of double and compression twins, exhibiting a much more evenly distributed and slightly wider orientation than that of basal parent grains and twins. In both Mg-2.9Zn and Mg-2.9Y alloys, a continuous texture weakening is observed with the progress of SRX, which results in a bimodal microstructure consisting of small TSRX grains and larger ones. With the increase in grain size during coarsening, the maximum intensity of basal pole figures rises linearly, with the slope of the lines being nearly identical in the two alloys. This texture strengthening was ascribed to the consumption of small TSRX grains by larger ones.