Buffett and Archer (2004) showed a model of the steady state global ocean clathrate reservoir that reproduces drill data and predicts a global methane inventory of about 5000 Gton C. The model inventory is very sensitive to ocean temperature, with factor-of-two changes in methane inventory in response to temperature changes of 1.5¿C. Here we explore the potential time-dependent behavior of the clathrate reservoir, assuming simple first-order rate constants for methane accumulation and meltdown in response to changes in the predicted steady state reservoir. For melting, we divide the reservoir into two parts, one melting catastrophically and the other slowly. Evolution of clathrates through geologic time is very sensitive to the choice of these rate constants. A positive feedback exists during a transient meltdown event, stronger if the catastrophic-melting fraction is high and its melting timescale is fast. A clathrate reservoir governed by such kinetics would melt down periodically, on a multimillion-year timescale determined by the rate constant for clathrate accumulation. Ideally, we would like a model that predicts runaway melting in the Paleocene and stability in the Pleistocene. However, the model is most unstable when climate is cold, rather than warm. Opting for stability in the Pleistocene constrains the melting kinetic parameters, leaving one degree of freedom. The grow-in timescale must be 5 Myr or longer, to get the deglacial δ13C right, but shorter than 10 Myr, in order for clathrates to have built up through geologically recent cooling. The model thus constrained predicts methane fluxes of 200 Gton C or less on deglaciations, but eventual releases of 2000--4000 Gton C in response to a ~2000 Gton C anthropogenic carbon release. Anthropogenic climate change differs from a deglaciation in that it warms the ocean to temperatures not seen in millions of years.