We discuss the nature of V Sagittae and T Pyxidis, two enigmatic blue variable stars commonly classed among the cataclysmic variables. These stars have bolometric luminosities in the range (1-50)x10^36 ergs s^-1, far exceeding that of any accretion-powered cataclysmic variable. They also show extremely blue colors (B-V=-0.3 and U-B=-1.3 after dereddening) and orbital light curves that are quite similar and yet are not seen in any normal cataclysmic variable. But in all these respects, as well as in the rich and highly excited emission-line spectrum, the stars provide a good match for the newly discovered class of ``supersoft'' X-ray binaries, probably powered by quasi-steady nuclear burning of accreted gas on a white dwarf. Both stars show photometric waves at the orbital period. V Sge also shows a deep minimum, a true eclipse of the accretion disk arising from fairly high binary inclination. T Pyx is nearly face-on (probably i~10^deg-20^deg), which results in narrow lines and a low amplitude for the orbital signal. T Pyx shows a very stable photometric wave at P=0.076227 days, but interpretation of this is hampered by another transient signal at 0.1098 days. This might be construed as evidence for a magnetic white dwarf.