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 \sim 3 \times 10 ^ { 30 } ~ { } erg~ { } s ^ { -1 } ( 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 .