Previous efforts to find evidence of deterministic nonlinear dynamics in the global geomagnetic system have treated the geomagnetic system as autonomous. However, the geomagnetic system is strongly driven by the stochastic solar wind. We consider the response of the magnetosphere, as given by the AE index, for one day when the IMF had a nearly constant southward value. Using both a series of non-linear statistics and non-linear prediction of the response to the input signal vBs, we find that there is some evidence for deterministic non-linear response of the Earth's magnetosphere on that day. ¿ American Geophysical Union 1993