Backscattering of Langmuir waves from low-frequency electrostatic waves in a plasma traversed by an electron beam is studied. The analysis is based on the use of beam electron, plasma electron, and ion susceptibilities provided by kinetic theory. For the case of a warm electron beam, formulae are derived for the growth rate and threshold associated with resonant backscattering from an ion-acoustic wave modified by the presence of the beam. For the case of a cold electron beam, formulae are derived from the growth rates associated with resonant back-scattering from a modified ion-acoustic wave and from a higher-frequency beam-plasma mode. A numerical study of the effects of an electron beam on these parametric instabilities is included.