An Equivalent Circuit Model (ECM) of a lithium ion (Li-ion) battery is an empirical, linear dynamic model and the bandwidth of the input current signal and level of non-linearity in the voltage response are important for the model's validity. An ECM is, however, generally parametrised with a pulse current signal, which is low in signal bandwidth (Part 1) and any non-linear dependence of the voltage on the current due to transport limitations is ignored. This paper presents a general modelling methodology which utilises the higher bandwidth and number of signal levels of a pulse-multisine signal to estimate the battery dynamics and non-linear characteristics without the need of a 3D look-up table for the model parameters. In the proposed methodology a non-parametric estimate of the battery dynamics and non-linear characteristics are first obtained which assists in the model order selection, and to assess the level of non-linearity. The new model structure, termed as the Non-linear ECM (NL-ECM), gives a lower Root Mean Square (RMS) and peak error when compared to an ECM estimated using a pulse data set. (C) 2016 Elsevier B.V. All rights reserved.