Abstract:Using the fourth-order Zakharov equation the theory of bifurcation by Sa-ffman & Yuen is extended to include the case where the modulation wavelength (p,q) = 0(1). Reasonable three-dimensional symmetrical wave patterns bifurcated from Stokes waves are obtained, and are in good agreement with those given by numerical results by Mclean (1982). Both critical amplitude and modulation wavelength are calculated. They are also close to the experimental data by Su (1981).