  Nonlinear stages of the recently uncovered instability due to insoluble
surfactant at the interface between two fluids are investigated for the case of
a creeping plane Couette flow with one of the fluids a thin film and the other
one a much thicker layer. Numerical simulation of strongly nonlinear longwave
evolution equations which couple the film thickness and the surfactant
concentration reveals that in contrast to all similar instabilities of
surfactant-free flows, no amount of the interfacial shear rate can lead to a
small-amplitude saturation of the instability. Thus, the flow is stable when
the shear is zero, but with non-zero shear rates, no matter how small or large
(while remaining below an upper limit set by the assumption of creeping flow),
it will reach large deviations from the base values-- of the order of the
latter or larger. It is conjectured that the time this evolution takes grows to
infinity as the interfacial shear approaches zero. It is verified that the
absence of small-amplitude saturation is not a singularity of the zero surface
diffusivity of the interfacial surfactant.
