This paper develops on-line nonlinear dynamic models of electrochemical supercapacitors which are for energy conversion and management. Based on the theory of electrochemical impedance spectroscopy, extensive alternative current impedance tests have been conducted to investigate the frequency-domain dynamics of these supercapacitors. A Nyquist diagram is plotted to help establish an equivalent electric circuit, which is regarded as the first-phase linear model. Two performance-influencing factors, environmental temperature and operating voltage, are considered as nonlinear effects. The nonlinear relationships among parameters of the capacitances and resistances in the first-phase model are established by a multi-layer artificial neural network. The neural parameters are trained using a back-propagation algorithm by feeding the experimental data bank. Combining the first-phase model and the on-line neural "parameter identifier", the algorithm produces an on-line nonlinear dynamic model. Simulation results have proved that this proposed model is able to achieve both system fidelity and computational efficiency. (C) 2011 Elsevier Ltd. All rights reserved.