To help understand the stability of cold, viscous boundary layers in geophysical contexts such as lava lakes and mantle convection, the following model problem is analyzed: Beneath a shear-free horizontal boundary, a thin layer of very viscous fluid overlies a deep layer of less viscous, less dense fluid. The initial unstable equilibrium is perturbed, and the growth of the disturbance is followed, including the nonlinear effects of large amplitude, by a long-wave analysis. The result shows that, in the final catastrophic growth, the peak thickness of the upper layer approaches infinity inversely proportional to the remaining time. (This conclusion also applies to fluids with power-law rheology.) Thus nonlinear effects greatly enhance growth. Keywords: Earth models. (EDC)