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In order to explain the anisotropic Rashba-Bychkov effect observed in several metallic-surface-state systems, we use k· p perturbation theory with a simple group-theoretical analysis and construct effective Rashba Hamiltonians for different point groups up to third order in the wave number. We perform relativistic ab initio calculations for the (3× 3) R 30∘ Bi/Ag (111) surface alloy, and from the calculated splitting of the band dispersion we find evidence of the predicted third-order terms. Furthermore, we derive expressions for the corresponding third-order Rashba parameters to provide a simple explanation of the qualitative difference concerning the Rashba-Bychkov splitting of the surface states at Au (111) and Bi/Ag (111).