To test whether climate forcings are additive, we compare climate model simulations in which anthropogenic forcings are applied individually and in combination. Tests are performed with different values for climate system properties (climate sensitivity and rate of heat uptake by the deep ocean) as well as for different strengths of the net aerosol forcing, thereby testing for the dependence of linearity on these properties. The MIT 2D Land-Ocean Climate Model used in this study consists of a zonally averaged statistical-dynamical atmospheric model coupled to a mixed-layer Q-flux ocean model, with heat anomalies diffused into the deep ocean. Following our previous studies, the anthropogenic forcings are the changes in concentrations of greenhouse gases (1860-1995), sulfate aerosol (1860-1995), and stratospheric and tropospheric ozone (1979-1995). The sulfate aerosol forcing is applied as a surface albedo change. For an aerosol forcing of -1.0 W/m$^2$ and an effective ocean diffusitivity of 2.5 cm$^2$/s, the nonlinearity of the response of global-mean surface temperatures to the combined forcing shows a strong dependence on climate sensitivity. The fractional change in decadal averages ($[(\Delta T_{G} + \Delta T_{S} + \Delta T_{O}) - \Delta T_{GSO} ]/ \Delta T_{GSO}$) for the 1986-1995 period compared to pre-industrial times are 0.43, 0.90, and 1.08 with climate sensitivities of 3.0, 4.5, and 6.2 $^o$C, respectively. The values of $\Delta T_{GSO}$ for these three cases are 0.52, 0.62, and 0.76 $^o$C. The dependence of linearity on climate system properties, the role of climate system feedbacks, and the implications for the detection of climate system's response to individual forcings will be presented. Details of the model and forcings can be found at http://web.mit.edu/globalchange/www/.