  The conditions under which stable evolution of two nonlinear interacting
waves are derived within the context of nematic crystals. Two cases are
considered: plane waves and solitons. In the first case, the modulation
instability analysis reveals that while the nonlocal term suppresses the growth
rates, substantially, the coupled system exhibits significantly higher growth
rates than its scalar counterpart. In the soliton case, the necessary
conditions are derived that lead the solitons to exhibit stable, undistorted
evolution, suppressing any breathing behavior and radiation, leading to soliton
mutual guiding.
