In our previous work we proposed some extensions of the Levenberg-Marquardt algorithm; the Bacterial Memetic Algorithm and the Bacterial Memetic Algorithm with Modified Operator Execution Order for fuzzy rule base extraction from input-output data. Furthermore, we have investigated fuzzy flip-flop based feedforward neural networks. In this paper we introduce the adaptation of the Bacterial Memetic Algorithm with Modified Operator Execution Order for training feedforward and fuzzy flipflop based neural networks. We found that training these types of neural networks with the adaptation of the method we had used to train fuzzy rule bases had advantages over the conventional earlier methods.