A real-time cell electronic sensing (RT-CES) system has been used for label-free dynamic measurements of cell responses to toxicant. Cells are grown onto the surfaces of the microelectronic sensors. Changes in cell number expressed as cell index (CI) have been recorded on-line as time series. The Cl data are used for dynamic modelling or parameter estimation for cell cytotoxicity process. We consider two dynamic modelling approaches, namely data-based system identification and first principle modelling. It is shown that data-based system identification can provide a quick solution for the cytotoxicity dynamic models and is effective for short-term predictions. It, however, can be poor for long-term predictions, particularly if there is no output correction, i.e., when the model is used for simulation. In view of this, the first principle modelling approach by considering fundamental physical principles such as toxicant transport is explored. For long-term prediction or simulation, the prediction performance for some of cytotoxicity process is dramatically improved using the models obtained from the latter approach. This happens only if the underlying mechanism is truly understood. Through several cytotoxicity modelling and validation studies, it is shown that the black box modelling and first principle modelling both should be considered in challenging modelling problems such as the cytotoxicity. Pros and cons of the two modelling approaches are discussed.