This paper presents a calculational procedure to determine the equilibrium phase for a given surface pressure pi. The monolayer is treated as orientationally free tails grafted to a two-dimensional net formed by the head groups of the amphiphilic molecules. The head groups form a subsystem with translational degrees of freedom characterized by strain variables in the plane of the surface, and the tail groups compose a subsystem characterized by rotational degrees of freedom. The order in the monolayer derives indirectly from the crystalline head groups through translational-rotational coupling. A stress-strain relation is derived which shows the energetically most favorable path for reorientation of the molecules due a a two-dimensional strain This set of strain stares for a given symmetry (phase) allows a contribution to the strain-state partition function to be computed. It is then straightforward to calculate the strain-state contribution to the free energy for a given phase and estimate the transition temperature between phases. (C) 1997 American Institute of Physics.