We calculated the elastic strain relaxation in(GaN)n-(AlN)n,(GaN)n(AlxGa1−xN)nand(GaN)n(InxGa1−xN)nsuperlattices wherenis the number of layers in the superlattice cell. This calculation and a similar calculation for a semiconductor–insulator–semiconductor structure allowed us to determine the lower and upper bounds for the elastic strain relaxation in(GaN)m(AlN)nsuperlattices with arbitraryn/mratios, i.e., we determine a full range of the critical thicknesses forGaNm(AlN)nsuperlattices. The obtained theoretical results can also be applied to other superlattices based on III nitrides and their solid solutions. Our theory agrees with the experimental data for GaN-AlN superlattices. Also, we show that the piezoelectric effect may cause a large shift of the absorption edge in defect-freeGaNm(AlxGa1−xN)nsuperlattices. ©1997 American Institute of Physics.