Abstract. The quality of the dimuon measurements made by NA60, in proton-nucleus and heavyion collisions, is much better than that reached by previous experiments, such as NA38 and NA50. The most important improvement is due to the use of a radiation-tolerant silicon vertex telescope, placed immediately downstream of the target. This allows NA60 to do a high quality measurement of φ meson yields and p T distributions. This paper presents results obtained in p-Be, p-In and p-Pb collisions at 400 GeV, from data collected in 2002, and in In-In collisions at 158 AGeV, as a function of centrality, from the 2003 running period. In particular, we show that the inverse m T slope measured in In-In collisions, in the φ µµ decay channel, increases with the number of nucleons participating in the collisions, rather than following a flat trend as seen in the NA50 data collected in the same decay channel but restricted to high p T values. We also show that our measurements seem to agree with the values previously measured by NA49, using φ KK decays, in Pb-Pb and other collision systems.