The problem of additional time reversal (TR) degeneracy and the transformation properties of ''time reversed' wave functions are investigated. In crystals the one electron Hamiltonian is invariant with respect to a space group of a crystal. The Bloch functions are the basis for irreducible representations (irrp's) of the wave vector groups k. When an irrp is complex the TR symmetry must be considered. Using Herring's criterion adopted to space groups we have investigated several hexagonal materials for optoelectronic devices such as ZnO, GaN, 6H-SiC. We have found many complex irrps. We discuss the effect of the TR on vibrational and electronic states together with optical selection rules in ZnO and GaN. In addition we list all complex irrps of the 32 crystallographic double point groups. Spin is taken into account throughout the whole discussion.