The light-scattering study of ripplon (thermally excited surface tension waves) was used to measure the surface elasticity of a myristic acid monomolecular film spread on a water surface in its coexisting state of two-dimensional liquid and vapor phases. The temperature dependence of the surface elasticity of both phases suggested that the critical behavior analogous to that of the usual three-dimensional fluids occurred in this two-dimensional system. The surface elasticity of the liquid phase decreased monotonously with temperature from 1.2x10[sup -2] N m[sup -1] at 20 (degrees)C to 2x10[sup -3] N m[sup -1] at 60 (degrees)C, while that of the vapor phase showed no appreciable difference from the value on a clean water surface. The Van der Waals equation of state specially reduced for the two-dimensional fluid was used to explain the result, and the (Pi)-A isotherms were theoretically calculated so that the surface elasticity predicted from these curves agrees well with the observed values. The two parameters characterizing the equation were determined, a=6.5x10[sup -39] N m[sup 3] and b=3.9x10[sup -19] m[sup 2], which are associated with effects of the attractive force and the excluded area, respectively. These values gave the critical temperature T[inf C]=85 (degrees)C.