Current stellar models predict fully convective structures for masses less than about 0.3 Mo. We have monitored low luminosity dMe and dM stars for flare activity with the 2.1 m telescope at McDonald Observatory. The dMe stars produced 2-5 detectable U-filter flares per hour while none were seen in the dM stars. Typically, 15-30% of the U-filter flux received from the dMe stars is due to flares. The flare activity level of dMe stars (on an absolute scale) decreases as one approaches the lower end of the main sequence. Non-linear frequency distributions of flare energy are seen in some binary flare stars, suggesting that both stars contribute to the ensemble of flares observed from the binary. Upper limits for the dM stars suggest activity levels about one thousand times smaller than in the dMe stars.