Set-membership identification of Hammerstein-Wiener models is addressed in the paper. First, it is shown that computation of tight parameter bounds requires the solutions to a number of nonconvex constrained polynomial optimization problems where the number of decision variables increases with the length of the experimental data sequence. Then, a suitable convex relaxation procedure is presented to significantly reduce the computational burden of the identification problem. A detailed discussion of the identification algorithm properties is reported. Finally, a simulated example is used to show the effectiveness and the computational tractability of the proposed approach.