Elemental abundances of two flares observed with the Solar Maximum Mission Flat Crystal Spectrometer are compared and contrasted. The first (a GOES Ml.5 flare) had a gradual rise and a slow decay, while the second (a GOES M5 flare) was much more impulsive. Simultaneous spectra of seven bright soft X-ray resonance lines provide information over a broad temperature range (2-35 x 10(6) K) and are available throughout both flares, making these events unique in the Solar Maximum Mission data base. Elemental abundances are investigated by means of a differential emission measure analysis. For the first flare, the plasma seemed to be characterized by coronal abundances but, for the second, the plasma composition could not be coronal, photospheric, or a linear combination of both. A good differential emission measure fit required enhanced neon such that Ne/O = 0.32 +/- 0.02, a value which is inconsistent with the current models of coronal abundances based on the elemental first-ionization potential, Similar values of enhanced neon are found for flaring plasma observed by the Solar Maximum Mission gamma-ray spectrometer, in He-3-rich solar energetic particle events, and in the decay phase of several long duration soft X-ray events. Sulfur is also enhanced in the impulsive flare, but not as dramatically as neon. These events are compared with two models which attempt to explain the enhanced values of neon and sulfur.