The double phase-conjugate mirror is an oscillator in the framework of the one-dimensional theoretical model previously used for its description. Results of a more consistent two-dimensional approach qualitatively differ from those of a one-dimensional analysis, indicating that the double phase-conjugate mirror is a convective amplifier. The correct physical picture of the scattering development is revealed, and the transverse profiles of scattered beams and the dynamics of nonlinear reflectivity are calculated.