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A radial-basis function neural network (RBFNN) has been used for modeling the dynamic nonlinear behavior of an RF power amplifier for third generation. In the model, the signal's envelope is used. The model requires less training than a model using IQ data. Sampled input and output signals were used for identification and validation. Noise-like signals with bandwidths of 4 and 20 MHz were used. The RBFNN is compared to a parallel Hammerstein (PH) model. The two model types have similar performance when no memory is used. For the 4-MHz signal, the RBFNN has better in-band performance, whereas the PH is better out-of-band, when memory is used. For the 20-MHz signal, the models have similar performance in- and out-of-band. Used as a digital-predistortion algorithm, the best RBFNN with memory suppressed the lower (upper) adjacent channel power 7 dB (4 dB) compared to a memoryless nonlinear predistorter and 11 dB (13 dB) compared to the case of no predistortion for the same output power for a 4-MHz-wide signal.