  We present XMM-Newton MOS imaging and PN timing data of the faint millisecond
pulsars PSR J0751+1807 and PSR J1012+5307. We find 46 sources in the MOS field
of view of PSR J0751+1807 searching down to an unabsorbed flux limit of 3 x
10^-15 ergs cm^-2 s^-1 (0.2-10.0 keV). We present, for the first time, the
X-ray spectra of these two faint millisecond pulsars. We find that a power law
model best fits the spectrum of PSR J0751+1807, Gamma=1.59+/-0.20, with an
unabsorbed flux of 4.4 x 10^-14 ergs cm^-2 s^-1 (0.2-10.0 keV). A power law is
also a good description of the spectrum of PSR J1012+5307, Gamma=1.78+/-0.36,
with an unabsorbed flux of 1.2 x 10^-13 ergs cm^-2 s^-1 (0.2-10.0 keV).
However, a blackbody model can not be excluded as the best fit to this data. We
present some evidence to suggest that both of these millisecond pulsars show
pulsations in this X-ray band. We find some evidence for a single broad X-ray
pulse for PSR J0751+1807 and we discuss the possibility that there are two
pulses per spin period for PSR J1012+5307.
