There has been much debate over the possibility that radiative cooling due to anthropogenic aerosols may substantially offset global warming from the enhanced greenhouse effect of raised atmospheric carbon dioxide levels. It is accepted that regional climates may alter if the net local forcing is non-zero. However, recent studies have alluded to the possibility of climate change even when the net radiative forcing from aerosols and carbon dioxide is very small. We present calculations demonstrating that even when the net radiative forcing of climate from simultaneous aerosol and CO2 perturbations at all locations is zero, heating rates within the atmosphere and surface radiation characteristics may still be substantially altered. Given the effect of radiative heating on atmospheric motions, and the dependence of biological systems on insolation, we conclude that the effects of possible climate change even when the mean radiative forcing at all locations is unchanged need to be quantified. Although an important quantity, the radiative forcing of climate should not be used as the sole indicator of possible climate change. ¿ 1997 American Geophysical Union