Abstract Group III-nitride materials such as GaN and AlN have attracted a great attention in researches on photonic devices that operate at short light wavelengths. The large band gaps of these materials turn them suitable for nanophotonic devices that operate in light ranges from visible to deep ultraviolet. The physical properties of wurtzite GaN and AlN such as their second and third order nonlinear susceptibilities, and their thermal and piezoelectric coefficients, also make them excellent candidates for integrate photonic devices with electronics, microelectromechanics, microfluidics and general sensing applications. Using a plane wave expansion method (PWE) the photonic band gap maps of 36 different two-dimensional photonic crystal lattices in wurtzite GaN and AlN were obtained and analyzed. The wavelength dependence and the effects of the material anisotropy on the position of the photonic band gaps are also discussed. The results show regions with slow group velocity at the edges of a complete photonic band gap in the M-K direction of the triangular lattices with circular, hexagonal, and rhombic air holes. Was also found a very interesting disposition of the photonic band gaps in the lattices composed of rhombic air holes.