A model for the effect of an electron beam on the drift cyclotron loss cone (DCLC) instabilities in mirror machines is presented. It is shown that because of the ponderomotive force of the beamgenerated plasmons, the growth rates of the DCLC instability are modified substantially. The model explains some of the observations on the Constance mirror machine where the DCLC instability was found to be quenched by the injection of an electron beam.