This paper presents a new approach to speed up the operation of time delay neural networks for fast detecting a word in a speech. The entire data are collected together in a long vector and then tested as a one input pattern. The proposed fast time delay neural networks (FTDNNs) use cross correlation in the frequency domain between the tested data and the input weights of neural networks. It is proved mathematically and practically that the number of computation steps required for the presented time delay neural networks is less than that needed by conventional time delay neural networks (CTDNNs). Simulation results using MATLAB confirm the theoretical computations.