This paper presents quasi-analytical solutions to a class of coupled atmosphere-ocean models for time-dependent ramp- and step-forced climate changes. The model consists of a conventional two-dimensional energy balance model of the atmosphere with an oceanic mixed layer coupled to a deep ocean having vertical heat transports due to horizontally uniform vertical diffusion and upwelling. The solution is partitioned into the particular or asymptotic part and the homogeneous or transient part. This partitioning facilitates understanding the different time constants involved in the problem. For ramp forcing there are two time constants: the lag time in the asymptotic straight line warming solution and the characteristic adjustment time to the asymptotic curve. The lag behind the ''no inertia'' warming is a few decades, while the adjustment time to the asymptotic curve is several hundred years due to the restructuring of the thermal profile near the main thermocline. This is in strong contrast to the step-forcing scenario where the adjustment time to the new constant steady state is only a few decades. The latter experiment suggests that step-forcing scenarios are not very similar to ramp-forcing scenarios. The model produces a warming of ~0.5 ¿C over the last hundred years provided the simulation is started 200 years ago. An interesting feature of the solutions is that the land surface areas lead the ocean surface areas in heating up by O(0.1 ¿C). This may lead eventually to a fairly robust signature of the greenhouse forcing. Future models of this type probably need more horizontal dependence on the vertical heat transport parameters as well as horizontal transport mechanisms. ¿ American Geophysical Union 1992