Using numerical simulation, we have investigated the generation of color solitons consisting of two radiation fragments with different carrier frequencies in a dual-wavelength laser. The proposed mechanism for the formation of such solitons involves nonlinear losses that increase with increasing intensity, the dispersion of the refractive index, spectral gain inhomogeneity, and the generation of a doublet radiation spectrum, owing to the corresponding spectral-dependent losses in the laser. The proposed theory explains the main features of the experimentally observed formation of color domains in fiber lasers and has the potential for further development of methods for controlling the nonlinear dynamics of laser radiation.