The difficulty associated with experimental studies of biochemical systems often makes the development of pure black-box neural network models particularly delicate. Hence, it is appealing to resort to a hybrid physical-neural network approach, which uses all the available a priori knowledge about the process, and combines a first-principles model with a partial neural network (NN) model describing the phenomena, which are (at least partly) unknown. In this work, this strategy is applied to a real-case experimental study, i.e. batch CHO animal cell cultures. Several alternative model formulations are considered, including serial model structures, in which neural networks are used to describe either the reaction kinetics or the complete reaction rates (globalizing pseudo-stoichiometry and kinetics), or parallel model structures, in which a NN compensates for the prediction errors of a first-principles model. Attention is focused on the procedure used to estimate the unknown NN parameters and initial conditions from experimental data, including a maximum likelihood approach to take account of all the measurement errors, and a weight decay technique to alleviate identifiability problems. The good model agreement is demonstrated with cross-validation tests. (C) 2004 Elsevier Ltd. All rights reserved.