We present the Rosat discovery of two new supersoft sources in the Lar
ge Magellanic Cloud (LMC), RX J0537.7-7034 and RX J0534.6-7056. The sp
ectra of both sources are consistent with a black-body temperature in
the range from 20 to 40 eV with corresponding X-ray luminosities in th
e range 10(38) - 5 X 10(36) erg s-1 respectively. A third known supers
oft source in the field of view, RX J0527.8-6954, was also detected at
a count rate level of about a factor of 4 lower than in the Rosat obs
ervations 2 years before. Together with Cal 83 and Cal 87, discovered
by the Einstein survey of the LMC, these five objects represent a new
class of X-ray sources. We discuss their interpretation in terms of th
e model of white dwarfs burning hydrogen rich material accreted from t
heir companion.