For geological periods lacking evidence of extensive glaciation, such as the Cretaceous, the presence of anomalously large, globally synchronous, cycles in coastal onlap stratigraphy (Haq et al., 1987) may be a new example of a nonlinear geophysical response to weak external forcing. A number of analogies can be drawn between this situation and the anomalously large 100-kyr late Pleistocene ice volume cycle vis-va-vis weak 100-kyr Milankovitch insolation changes. Apropos of these analogies we discuss formal models for evolving, free, sedimentary or glacial surfaces, subject to lateral mass transport and subsidence, and observe that nonlinear diffusivity obtains in each case. In particular, the systems both involve retarded transport. We then define equilibrium surfaces and show them to be closely related to either the subsidence profile or the ablation profile. In the absence of mass supply feedback, these equilibrium surfaces should be unconditionally stable, and amplified response to external forcing are unlikely. We then consider feedbacks on mass supply and show first how to construct a three-variable glacial wedge that freely oscillates. Glacial models of this type suggest that a fundamental role is played in the oscillation by isostatic relaxation times. This effect should be considered for sedimentary systems as well. We finish with a speculation about a simple sediment supply feedback that might be associated with relative sea level changes and illustrate graphically how the multiple equilibrium points introduced by this feedback could lead to large coastal onlap shifts from relatively small perturbations to the system. Much more work will be needed, however, to determine the parameter values required to achieve such behavior and if such values are physically realistic. ¿American Geophysical Union 1991