We present spectroscopy and photometry of the LMC supersoft binary sys
tem RX J0513.9-6951. We derive a refined spectroscopic period of P = 0
.761 +/- 0.004 day, which is consistent with the value obtained from l
ong-term photometric monitoring (P = 0.76278 +/- 0.00005 day). We see
bipolar outflow components of He II and H beta, with velocities of sim
ilar to 3800 km s(-1), strongly suggesting that the compact object is
a white dwarf. Using all the available optical and X-ray data, we cons
truct a theoretical model to explain the principal features of the unu
sual variability of this source. In particular, we note that X-ray out
bursts have only been seen at times of optical minima. From this, we c
onclude that the most likely cause of the X-ray outbursts is a photosp
heric contraction during a nuclear shell burning phase, rather than a
thermonuclear flash or shocked emission. The system probably comprises
a relatively massive white dwarf accreting at a high rate (similar to
10(-6) M(.) yr(-1)) from an evolved donor star and is observed close
to pole-on.