Abstract: There can exist two kinds of ion-acoustic waves in a plasma, i.e. fast mode and slow mode, if the plasma consists of two ion species which masses are greatly different from each other. Fast and slow mode are mainly due to the motions of light ions and heavy ions, respectively. A systematic perturbation method is used to analytically calculate the frequencies and damping rates of the two modes. The method developed by McKinstrie et al, is based upon the expansion of plasma dispersion relation in a power series of Ti /Te, where Ti,e are te ion and electron temperatures. Comparing with the results obtained from numerical solution shows that the formulae obtained in this paper can give more accurate results than previous studies, such as presented by Williams et al.