Résumé : In this paper, we propose an Arbitrary Lagrangian Eulerian (ALE) formulation of the Generalized Navier Boundary Condition introduced in~\cite{qian-wang-sheng-03,qian-wang-sheng-06} to model the displacement of the contact line of an interface in two-fluid flows. Owing to these boundary conditions, it is possible to circumvent the incompatibility between the classical no-slip boundary condition and the fact that the contact line of the interface on the wall is actually moving. We present some results on the stability of the numerical scheme in energy norm. We show the validity of the approach by numerical experiments on two-fluid flows in narrow channels.