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We prove existence of a wetting transition for two classes of gradient fields which include: (1) The Continuous SOS model in any dimension and (2) The massless Gaussian model in dimension 2. Combined with a recent result proving the absence of such a transition for Gaussian models above 2 dimensions (Bolthausen et al., 2000.) J. Math. Phys. to appear), this shows in particular that absolute-value and quadratic interactions can give rise to completely different behavior.