The microstructural evolution of the CuZnAl shape memory alloys was studied by indirect techniques relating to the atomic migration rate of grain boundaries. Addition elements were used in a Cu-15,5Zn-8,0Al alloy to provide a comparison with the same alloy without microelement additions. The alloys were melted in an induction furnace of 24 kVA. After casting, the bulk samples of the alloys were homogenized. Then they were solution treated and hot-rolled followed by water-quenching to initiate the recrystallization. Finally, annealing produced at different temperature ranges was made in different samples in order to establish a law for the grain growth. Following the heat treatments, all annealed samples were examined by statistical metallography and the grain sizes were measured. After measurements, the same empirical law of grain growth was found for the different alloys and the ln [D-Do] x 1/T diagrams were plotted in order to establish the kinetic behavior. Based on the estimated values of the activation energy, important conclusions were obtained concerning the addition elements.