Exciton binding energies and the nonlinear optical properties in wurtzite GaN and ZnO wide band gap semiconductor quantum dots are investigated with the same barrier height of both the materials. The interband emission as a function of dot radius is studied. The effects of strain, including the hydrostatic and the biaxial strain and the internal electric field, induced by spontaneous and piezoelectric polarization are taken into account in all the calculations. Numerical calculations are performed, using variational procedure within the single band effective mass approximation. Some nonlinear optical properties are studied in GaN/Ga(0.8)A1(0.2)N and ZnO/Zn0.607Mg0.393O quantum dots taking into account the strain-induced piezoelectric effects. Our results show that the nonlinear optical properties strongly depend on the geometrical confinement.