VLA observations of narrow-band behavior in 20 cm flares from two red dwarf stars, L726 - 8A and AD Leo, are reported. The flare on L726 - 8A was observed at 1415 and 1515 MHz; the flux and the evolution differed significantly at the two frequencies. The flare on AD Leo lasted for 2 hr at 1415 MHz but did not appear at 1515 MHz. The AD Leo flare appears to rule out a source drifting through the stellar corona and is unlikely to be due to plasma emission. In the cyclotron maser model the narrow-band behavior reflects the range of magnetic fields present within the source. The apparent constancy of this field for 2 hr is difficult to understand if magnetic reconnection is the source of energy for the flare. The consistent polarization exhibited by red dwarf flares at 20 cm may be related to stellar activity cycles, and changes in this polarization will permit measuring the length of these cycles.