The propagation of solitons in dissipative, elliptically birefringent single-mode fibres is considered analytically by a variational technique, in terms of a theoretical model of two coupled nonlinear Schrödinger equations with all the oscillating terms, arising from nonlinear polarization. For nearly equal amplitudes of the interacting solitons of different polarizations, the frequency of relative oscillations of soliton positions has been determined.