We have investigated the wurtzite and hexagonal compounds (w- and h-BN, AlN, ZnO) under various compression conditions using the first-principles molecular dynamics (FPMD) method. Applying anisotropic compression is an important approach for the investigation of novel material properties. We found remarkable changes in the internal parameters u of all calculated wurtzite compounds under uniaxial c-axis compression (P_z) within the symmetry constraint. The internal parameter u of the wurtzite structure increased as the pressure increased and finally became 0.5, resulting in a phase transformation into a hexagonal structure. Transition pressures for BN, AlN and ZnO under c-axis compression are 300–325, 15–20, 5–10 GPa, respectively. The value of the transition pressure of BN (wurtzite → hexagonal) was found to be significantly higher than those of the other two compounds (AlN, ZnO) in which the crystal structure of BN could be broken under the large uniaxial compression. The changes in the electronic band structure and the lattice properties (lattice constant, c⁄a ratio, volume of the unit cell) of BN in the wurtzite-to-hexagonal transformation were also quite large and unusual. These results imply that the wurtzite-to-hexagonal transformation of BN is unlikely to occur. In contrast, the changes in the lattice properties of AlN and ZnO were small because of their low transition pressures (5–20). These lower transition pressures are mainly due to larger ionicity of AlN and ZnO.