Abstract The dynamics of complex spectral properties of two frequency harmonic undulator radiations along on and off axis has been analytically investigated using the techniques of generalized Bessel functions. The relativistic electron beams with non negligible energy spread results in degradation in brightness and gain. The effect of energy spread on two frequency harmonic undulator (TFHU) radiations and on axis gain has been analyzed. Maximum acceptable r.m.s. value of energy spread has been determined to support the complex spectral pattern of radiation and gain.