Multistability of Langmuir monolayers, in particular those composed of fatty acids, is reflected by a very rich and complicated phase diagram. We argue that strain-tilt-backbone coupling determines the behavior described by that diagram. Following the solid state approach, we show that a natural order parameter set is defined by thermal averages of spherical harmonics and strain tensor components. In addition, we show that the backbone order parameter can be conveniently represented by an elastic dipole tensor. Treating Langmuir monolayers as disordered solids, we have derived an orientational entropy contribution to the free energy. The swiveling transition between L-2(L-2h) and L-2＇( L-2*) phases is discussed in detail and is conveniently described in terms of the proposed order parameters. We discuss why the change in the distortion direction of the 2D unit cell tracks the change in tilt direction of the molecules, and also why the cell dimensions involved in the swiveling transition are the same in both phases.