ABSTRACTThe depinning of a contact line is studied as a dynamical critical phenomenon by a functional renormalization group technique. In D = 2 - ∈ “line” dimensions, the roughness exponent is ζ = ∈/3 to all orders in perturbation theory. Thus, ζ = 1/3 for the contact line, equal to the Imry-Ma estimate for equilibrium roughness. The dynamical exponent is z = 1 – 2∈/9 + O(∈2) < 1, resulting in unusual dynamical properties. In particular, a characteristic distortion length of the contact line depinning from a strong defect is predicted to initially increase faster than linearly in time. Some experiments are suggested to probe such dynamics.