This paper presents, for the first time, an analysis of space plasma turbulence based on the NARMAX system identification approach. Fundamental nonlinear processes in the low-frequency turbulence observed in the terrestrial foreshock by Active Magnetospheric Particle Tracer Explorers United Kingdom Satellite (AMPTE UKS) and Ion Release Module (AMPTE IRM) are studied using time domain identification methods developed for nonlinear dynamical systems. It is shown, directly from the experimental data, that the cubic nonlinearity has a significant influence on the steepening of the nonlinear low-frequency waves and on the dependence of the phase velocity upon the wave amplitude. In comparison with a previous frequency domain approach, the present method requires only short data sets. ¿ 2001 American Geophysical Union