Interface models have been developed over the past 10 years for simulating various scales of composite debonding e€ects, such as decohesion between matrix and ®bers and delamination in laminates, formulated with and without rate dependencies. We give several examples of how sudden``sudden``solution jumps'' can occur in rate-independent models like the Tvergaard depending on the geometry, interface behavior, and ®nite element discretization. This kind of instability disappears for the often-used viscous models, but the result is a high rate dependency that deviate from experimental trends. A new kind of viscous regularization is proposed here, which applies to the Tvergaard debonding model or modified ones, and has a limited rate dependency. A few simple examples are given, including the delamination of a double cantilever beam, to show the capabilities of the technique proposed.