A systematic and comprehensive study of linear and nonlinear analyses of the propagation of low-frequency modes in two-ion-species plasma has been made. Two new non-propagating modes on different ion time-scales are reported. These modes are excited by nonlinear coupling with the external pump. The threshold field of the pump and the growth rates of the various modes above the threshold are also calculated. A comparison of the results with those of single-ion-species plasma shows that the non-propagating mode on the fast ion time-scale excites the oscillating two-stream instability. In addition, the mode corresponding to ωr = 0 on the slow ion time-scale becomes important nonlinearly and excites a new type of instability. It is interesting to note that the threshold electric fields excitation of these instabilities are the same.