The propagation of waves in weakly dissipative plasmas is investigated. A new expression for the wave energy flux is obtained, which is proportional to ´mode/k, where ´modeis the real part of the eigenvalue of the dispersion tensor corresponding to the wave mode. Significant differences from the usual definition of dielectric wave energy flux occur in case of a non-negligible anti-Hermitian contribution to the dielectric tensor. This occurs, for example, near electron cyclotron resonance. The direction of the corrected wave energy flux is consistent with that of the trajectory of a wave beam crossing the EC resonance as obtained in Westerhof (Westerhof E 1997 Plasma Phys. Control. Fusion391015). It is shown that ray-tracing near cyclotron resonance can be performed with the use of ´modeas ray-Hamiltonian.