A method is presented for transforming a local-linear prediction model into dynamical analogues of the coupling between the input and output data that enters and forms the prediction model. Two types of analogues are produced: (1) local-linear analogues composed of readily recognized physical components and (2) nonlinear analogues suitable for prediction purposes; both are data derived. Second-order analogues of the magnetospheric dynamics are examined in detail using the composite ISEE 3 solar wind parameter VBs for input and simultaneous Dst index data for output. An optimized local-linear analogue is constructed which minimizes the rms difference between analogue output and measured Dst. It is shown that the optimized local-linear analogue reduces, in behavior, to that of the first-order Burton et al. [1975> Dst model during periods of Dst recoveries, both large and small. During those periods, however, the analogue effectively decouples from the solar wind VBs driver. At other times the coupling strength is found in general agreement with the value deduced by Burton et al., but, at those times, the analogue behavior is beyond the scope of their first-order equation. Nonlinear analogues are also constructed and studied. These are driven, damped, harmonic oscillators in which the dissipation rate, restoring force, and coupling strength to the VBs driver are expressed as functions of the Dst and VBs variables; these expressions are data derived. It is found that these analogues couple to the solar wind through the expression (VBs/Dst)VBs, rather than through the usual linear dependence on VBs. The suitability of these nonlinear analogues for prediction purposes is discussed. ¿ 1997 American Geophysical Union