We examine the dependence of the Dst timescales on storm conditions and its implications for the storm-substorm relationship. The growth, decay and oscillation timescales are expressed as functions of the storm magnitude and phase, and the solar wind electric-field input VBs. Nonlinear, second-order autoregressive moving average (ARMA) models are fit to 5-min data and yield two timescales, an exponential decay with an average e-folding time &tgr;1=-4.69 hours (-7.26 hours for the pressure-corrected Dst(0)) and an inductive time &tgr;2=-0.81 hours (-0.05 hours for Dst(0)). Around these average values there is a systematic variation: (1) For most of the storm duration, &tgr;1 is negative representing the rapid adjustment of the inner magnetosphere to the imposed electric field. (2) In the early main phase, however, &tgr;1=5.29 hours (1.76 hours for Dst(0)), so the disturbance grows as a slow exponential. (3) During commencement and main phase, the timescales are complex conjugate and the response is oscillatory. Fast oscillations during storm commencement (period 1.13 hours; 8.48 min for Dst(0)) are a ringing response to interplanetary pressure enhancements. Slow oscillations in the main phase have an average period of 1.96 hours (1.55 hours for Dst(0)) and coincide with AL intensifications. The main phase can be separated into periods of oscillatory, fast decay (coincident with AL activity and probably due to injections) and monotonic slow decay (regular convection). (4) All timescales decrease with increasing interplanetary activity because high activity involves acceleration and loss of heavy ions with shorter lifetimes than protons. (5) Also, decay times are about twice as long during recovery than during main phase. (6) Similar dependences are found for the solar wind coupling coefficients. The models are similar to linear models in predictability and are stable with respect to perturbation in the initial conditions. ¿ 1999 American Geophysical Union