  We present the results of a 50 ks long X-ray observation of the relativistic
double pulsar system PSR J0737-3039 obtained with the XMM-Newton satellite in
March 2004. The source has a soft spectrum (power law photon index =
3.5(+0.5,-0.3)) and a 0.2-10 keV luminosity of ~3x10^30 erg/s (assuming a
distance of 500 pc), consistent with the values derived from a previous Chandra
observation. No flux variations have been detected, implying the absence of
large orbital modulations. The high time resolution of the EPIC instrument has
allowed us to perform the first search for X-ray pulsations from this system.
The result was negative, with an upper limit of 60% on the pulsed fraction of
the 22 ms pulsar.
