Generalized fractional Maxwell model is applied to simulate the creep and the relaxation behavior of PEEK and PPS measured at different aging stages and different temperatures. Genetic algorithm and the conjugated gradient method are combined to optimize the model parameters. The results show that the fractional Maxwell model can describe both the creep and relaxation data very well when the model parameters are fitted properly. The momentary creep compliance and the relaxation modulus change with the time at an increasing rate; the fractional orders of the two fractional elements building up the model correspond to the creep or relaxation exponents at the initial glassy stage and the terminal fluid state. The relaxation time tau of the model, which corresponds to the characteristic time of alpha transition of the sample, shifts towards longer time with increasing the aging time and lowering the aging temperature. In the time domain scaled by the relaxation time tau, all the creep or relaxation curves measured at different aging times and temperatures superpose automatically, which means the time-aging time superposition and the time-temperature superposition present themselves. The shift rates and the temperature shift factors can be then obtained from the model parameters. Good simulation for the creep and relaxation behavior and optimum superposition of the experimental data achieved by the fractional model may offer reliable predictions for the long-term stress-strain response. (C) 2012 Elsevier Ltd. All rights reserved.