The strong correlation between magnetic storms and southward interplanetary magnetic field (IMF) is well known from linear prediction filter studies using the Dst and IMF data. However, the linear filters change significantly from one storm to another and thus are limited in their predicting ability. Previous studies have indicated nonlinearity in the magnetospheric response as the ring current decay rate varies with the Dst value during storms. We present in this letter nonlinear models for the evolution of the Dst based on the OMNI database for 1964--1990. When solar wind data are available in advance the evolution of storms can be predicted from the Dst and IMF data. Solar wind data, however, are not available most of the time or are available typically an hour or less in advance. Therefore, we have developed nonlinear predictive models based on the Dst data alone. In the absence of solar wind data, these models cannot predict the storm onset, but can predict the storm evolution, and may identify intense storms from moderate ones. The input-output model based on IMF and Dst data, the autonomous model based on Dst alone, and a combination of the two can be used as forecasting tools for space weather. ¿ American Geophysical Union 1996