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Adaptive channel equalisers compensate the disruptive effects caused by band-limited channels, hence enabling higher data rate in digital communication. Designing efficient equalisers based on low structural complexity is an area of interest amongst communication system designers. This research has significantly contributed to the development of novel equaliser structures in the neural network paradigm on the framework of both the feedforward neural network and the recurrent neural network of low structural complexity. Various innovative techniques like hierarchical knowledge reinforcement, genetic evolutionary concept, transform domain approach, tuning of sigmoid slope of neuron using fuzzy logic concept have been incorporated into an FNN framework to design highly efficient equaliser structures. Subsequently, an hybrid concept of using cascaded modules of RNN and FNN in various configurations has also been proposed. Significant performance improvement over the conventional equalisers in terms of BER, faster adaptation rate and ease of implementation are the major advantages of the proposed neural network based equalisers.