The optical properties of Cu - Mn alloys with Mn concentrations of 2, 5, 10 and 17,5 % (which corresponds to the <$Egamma>-solid solutions) were studied within a wide spectral range of 0,23 to 2,8 <$Emu>m (0,44 - 5,39 eV). Real and imaginary parts of the refractive index were measured, other optical properties such as dielectric constant, optical conductivity and the coefficient of specular reflectance at normal incidence were calculated being based on them. The analysis of the dispersion dependences <$Eepsilon (h nu )>, <$ER(h nu )> and <$Esigma (h nu )> enabled us to offer the electronic structure model for these alloys. According to this model, the electronic spectra (dependence of the density of electronic states on energy N(E)) of alloys with the indicated concentrations of components are the superposition of electronic spectra of Cu host, with weights equal to Cu concentrations, and the density of states within the impurity band, calculated using the experimental data.