The existence of localized regions of intense lower hybrid waves in the auroral ionosphere recently observed by rocket and satellite experiments can be understood by the study of a non-linear two-timescale coupling process. Such type of wave-wave interactions was first described by Musher and Sturman [1975>. In this Letter, we demonstrate that the leading non-linear term in the standard Musher-Sturman equation vanishes identically in strict two-dimensions (normal to the magnetic field). Instead, the new two-dimensional equation is chacterized by a much weaker non-linear term which arises from the ponderomotive force perpendicular to the magnetic field, particularly that due to the ions. The old and new equations are compared by means of time-evolution calculations of wave fields. The results exhibit a remarkable difference in the evolution of the waves as governed by the two equations. Such dissimilar outcomes motivate our investigation of the limitation of Musher-Sturman equation in quasi-two-dimensions. We show that the equation may be applicable only if k∥2/k⊥2≫&ohgr;2/&OHgr;2e, where &ohgr;2≲&ohgr;2A or &OHgr;2i. In addition, assumptions of quasi-steady slow-mode respnses by ions and electrons require &ohgr;2/k2&ngr;i2 and &ohgr;2/k∥2v2e≪1 respectively. Only within all these limits can Musher-Sturman equation adequately describe the collapse of lower hybrid waves. ¿American Geophysical Union 1995