Global temperature responses from different abrupt CO2 change experiments participating in Coupled Model Intercomparison Project Phase 6 (CMIP6) and LongRunMIP are systematically compared in order to study the linearity of the responses. For CMIP6 models, abrupt-4xCO2 experiments warm on average 2.2 times more than abrupt-2xCO2 experiments. A factor of about 2 can be attributed to the differences in forcing, and the rest is likely due to nonlinear responses. Abrupt-0p5xCO2 responses are weaker than abrupt-2xCO2, mostly because of weaker forcing. CMIP6 abrupt CO2 change experiments respond linearly enough to well reconstruct responses to other experiments, such as 1pctCO2, but uncertainties in the forcing can give uncertain responses. We derive also a generalised energy balance box model that includes the possibility of having oscillations in the global temperature responses. Oscillations are found in some models, and are connected to changes in ocean circulation and sea ice. Oscillating components connected to a cooling in the North Atlantic can counteract the long-term warming for decades or centuries and cause pauses in global temperature increase.