The influence of four basic relaxation mechanisms on two‐component plasma waves is examined. The analysis stems from a set of generalized macroscopic equations that include two self‐relaxation mechanisms in addition to terms which dampen difference in temperatures and difference in flows between the gases. The emergent dispersion relation is diagonal with respect to longitudinal and transverse components of the state vector. The longitudinal relation is linear in the temperature coupling parameter while the transverse relation is independent of the self‐relaxation rates and the difference in velocity relaxation rates. The longitudinal determinant yields well‐known roots in the limit of long temperature relaxation times, while in the opposite limit new relations are obtained.