DESY-HERA. Measurement of cross sections for dijet diffractive photoproduction in the interactions of 27.5 GeV electrons and positrons with 920 GeV protons at Q**2 < 1 GeV, Y from 0.20 to 0.85 and X(POMERON) < 0.025. The analysis required the ET of the highest ET jet to be greater than 7.5 GeV and the second highest greater than 6.5 GeV with both jets having pseudorapidity in the range -1.5 to 1.5. The data at a centre of mass energy of 318 GeV were collected during the 1999-2000 running period with integrated luminosities of 12.1 pb-1 for electron and 65.1 for pb-1 positron collisions. The second DSYS error is due to the uncertainty in the jet energy scale.