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 \times 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 \pm 0.20 , with an unabsorbed flux of 4.4 \times 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 \pm 0.36 , with an unabsorbed flux of 1.2 \times 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 .