In the four-wave-mixing process in a two-mode optical fiber, where the pump power is divided between the LP(01) and LP(11) modes, the Stokes or anti-Stokes wave can evolve in either of the two modes, depending on the sign of the group-delay difference between the modes. This process provides a simple means to determine accurately the wavelength at which the group velocities of the two modes of the fiber are equal. Experimental results obtained with a tunable pulsed dye laser as the pump source are presented and discussed for several short fibers.