Using a kinetic theoretical approach, the characteristics of electron acoustic waves (EAWs) are investigated in plasmas whose electron velocity distributions are modeled by a combination of two kappa distributions, with distinct densities, temperatures, and kappa values. The model is applied to Saturn's magnetosphere, where the electrons are well fitted by such a double-kappa distribution. The results of this model suggest that EAWs will be weakly damped in regions where the hot and cool electron densities are approximately equal, the hot to cool temperature ratio is about 100, and the kappa indices are roughly constant, with kappa(c) similar or equal to 2 and kappa(h) similar or equal to 4, as found in Saturn's outer magnetosphere (R similar to 13-18 R-S, where R-S is the radius of Saturn). In the inner magnetosphere (R < 9 R-S), the model predicts strong damping of EAWs. In the intermediate region (9-13 R-S), the EAWs couple to the electron plasma waves and are weakly damped.