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Two different neural network architectures were designed for speaker independent phoneme recognition systems. The first architecture consists of the Radial Basis Function (RBF), while in the second architecture a Self-Organising Maps (SOM) neural network replaces the RBF. The Discrete Wavelet Transform (DWT) is used for feature extraction in both systems. Both systems were tested on the TIMIT database. The highest recognition rates obtained are 36.3% and 46.7%, for the RBF and SOM architectures respectively for multi-speaker unlimited vocabulary speech.