Three approaches to the problem of Neural Network (NN) modelling of chemostat microbial culture accounting for the memory effects are considered and, based on the results they are compared. The first approach uses feedforward NNs with time delay feedback connections from and to the output neurons, for the entire process modelling. The second and third approach relay on Hybrid NN modelling. The second one applies feedforward NNs with time delayed inputs for the specific growth rate approximation within the framework of the classical unstructured model. In this case the specific consumption rate is assumed to be proportional to the specific growth rate. The yield factor is assumed to be constant or polynomial function of the substrate concentration. The third approach is also based on a classical unstructured model, but different feedforward NNs with delay elements for both specific growth rate and specific consumption rate approximation are adopted. On the example of the growth of a strain Saccharomyces cerevisiae on a glucose limited medium different NN topologies are studied and a suitable model is figured out.