Linear and nonlinear analysis of the propagating and nonpropagating mo
des in a two-electron temperature plasma has been made. The high frequ
ency electron acoustic modes are found to exist on fast w/k > C(c), C(
h) and slow C(h) > omega/k > C(c) electron time scales. The threshold
value and growth rates for delta > > omega(r) are derived. The nonprop
agating mode is the oscillating two-stream instability which may exist
in Solar type III radio bursts.