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It is argued that some phase--transitions observed in models ofnon-equilibrium wetting phenomena are related to contact processes withlong-range interactions. This is investigated by introducing a model where theactivation rate of a site at the edge of an inactive island of length $\ell$ is$1+a\ell^{-\sigma}$. Mean--field analysis and numerical simulations indicatethat for $\sigma>1$ the transition is continuous and belongs to theuniversality class of directed percolation, while for $0<\sigma<1$, thetransition becomes first order. This criterion is then applied to discusscritical properties of various models of non--equilibrium wetting.Comment: 12 Figures. V Version resubmitted to Phys. Rev. E after referees  repor

Directed percolation with long-range interactions: Modeling nonequilibrium wetting