Neural networks add flexibility to the design of equalizers for digital communications. In this work novel, decision-feedback (DF) neural equalizers (DFNE) are introduced and compared with classical DF equalizers and Viterbi demodulators. It is shown that the choice of a cost functional based on the Discriminative Learning (DL), coupled with a fast training paradigm, can provide neural equalizers that outperform the standard DF equalizer (DFE) at practical signal to noise ratio (SNR). Resulting architectures are competitive with the Viterbi solution from cost-performance aspects.