We suggest that, close to the time of maximum luminosity in both solar and stellar flares, the ratio of thermal X-ray luminosity, L/sub x/, to optical luminosity, L/sub v/, is given by the ratio of radiative to conductive energy loss rates from the X-ray flare plasma. This leads to values of L/sub x//L/sub v/ in UV Ceti which may be more than an order of magnitude smaller than the mean value L/sub x//L/sub v/ in solar flares. Scaling from solar flares may therefore lead to overestimates of the X-ray fluxes expected in stellar flares. Our results are consistent with recent detection of X-rays from a large flare on UV Ceti. According to our treatment, the light curve of an optical stellar flare has a decay time which is determined not by radiative recombination but by the time scale for heat conduction from the X-ray plasma. With this interpretation, stellar flare plasma is found to have a density no less than approximately 6 x 10/sup 10/ cm/sup -3/. Temperatures in stellar flare plasma are probably in the range (1--4) x 10/sup 7/ K, similar to solar flares. (AIP)