Power competition effect is investigated in two channel dye laser system working at two wavelengths with continuously variable polarization states. As a intracavity beam divider, both a knife edge beam divider and a half mirror beam divider are used. The former has no competition effect between the two outputs at wavelengths, whereas the latter has significant power competition effect. The gain and relative power competition effect are measured in two wavelengths oscillation using half mirror beam divider. The spectroscopic analysis of the laser output shows complicated structures within the gain profile. Explanation of these experimental results seem requiring further detailed work.