The effective electron and hole masses are fundamental quantities of semiconductors, used in numerous analyses of experiments and theoretical investigations. We present calculations of the band structure near the band edges in intrinsic GaN and AIN, both for the wurtzite and the zinc-blende polytypes. We have utilized a full-potential linearized augmented plane wave method within the density functional theory and with two different exchange-correlation potentials. The lattice parameters have been determined by a minimization of the total energy, whereupon the crystal-field splitting, the spin-orbit splitting, and the effective electron and hole masses have been calculated. The calculated effective masses are in good agreement with available experimental values. We show the importance of performing a fully relativistic calculation. For instance, the hole mass in cubic AIN is a very large and negative quantity if the spin-orbit coupling is excluded, whereas the fully relativistic calculation gives a relatively small and positive value.