We investigate the use of an approximate minimum bit error rate (MBER) approach to multiuser detection using recurrent neural networks (RNN). We examine a stochastic gradient adaptive algorithm for approximating the MBER from training data using RNN structures. A comparative analysis of linear and neural multiuser receivers (MUD), employing minimum mean squared error (MMSE) and approximate MBER (AMBER) adaptive algorithms is carried out. Computer simulation experiments show that the neural MUD operating with a criterion similar to the AMBER algorithm outperforms neural receivers using the MMSE criterion via gradient-type algorithms and linear receivers with MMSE and MBER techniques.