A comparative study of nonlinear behavioral models with memory for radio-frequency power amplifier (PAs) is presented. The models are static polynomial, parallel Hammerstein (PH), Volterra, and radial basis-function neural network (RBFNN). Two PAs were investigated: one was designed for the third-generation (3G) mobile telecommunication systems and one was designed for the second-generation (2G). The RBFNN reduced the total model error slightly more than the PH, but the error out of band was significantly lower for the PH. The Volterra was found to give a lower model error than did a PH of the same nonlinear order and memory depth. The PH could give a lower model error than the best Volterra, since the former could be identified with a higher nonlinear order and memory depth. The qualitative conclusions are the same for the 2G and 3G PAs, but the model errors are smaller for the latter. For the 3G PA, a static polynomial gave a low model error as low as the best PH and lower than the RBFNN for the hardest cross validation. The models with memory, PH, and RBFNN, showed better cross-validation performance, in terms of lower model errors, than a static polynomial for the hardest cross validation of the 2G PA.