We report an investigation of the statistical fluctuations of the two-mode laser output as the asymmetry parameter is varied. The above results relate to computer solutions of the coupled Langevin equations both with and without pumping fluctuations. We find that as the asymmetry parameter is changed positively, the mean intensity of one mode is increased because the normalized intensity auto-correlation is decreased so that the natural dwell time is lengthen. The laser output does respond to a sinusoidally injected asymmetry parameter for small pump parameter.