High-field magnetisation and high-pressure resistivity measurements have been performed on monocrystalline samples of the superconducting compound URu2Si2 just above Tc. At 1.4 K, well below the magnetic ordering temperature of about 17.5 K, two sharp transitions at 36 and 40 T have been observed in the magnetisation versus field curves along the tetragonal c-axis, whereas the a-axis magnetisation curve remains linear up to 40 T. These transitions point to a complex magnetic behaviour. Above the second transition the magnetic moment per uranium atom exceeds a value of 1.3 μB. The resistivity versus temperature curve is distinguished by two characteristic temperatures of 75 and 17.4 K, corresponding with the onset of coherent scattering and the magnetic transition, respectively. Both characteristic temperatures increase with pressure.