By using the theory of partially coherent light and the basis set of biorthogonal elegant Hermite-Gaussian (EHG) modes,the analytical expressions for the mode coherence coefficients (MCCs) and M2-factor of laser light have been derived. The relation between the coherent-mode representation of laser beams in terms of EHG modes and that in terms of corresponding standard Hermite-Gaussian (SHG) modes has been built up. Furthermore,two typical application examples have been discussed. It can be shown that the MCCs in EHG coherent-mode representation can be obtained by use of the MCCs in SHG coherent-mode representation;for the case of the modes with the same orders having the same weight factors,the beam quality of the laser beams that are made up of a superposition of mutually uncorrelated EHG modes is better than that of mutually uncorrelated SHG modes.