Pluto's first known satellite, Charon, was discovered in 1978. It has a diameter (~1,200km) about half that of Pluto, which makes it larger, relative to its primary, than any other moon in the Solar System. Previous searches for other satellites around Pluto have been unsuccessful, but they were not sensitive to objects <~150km in diameter and there are no fundamental reasons why Pluto should not have more satellites. Here we report the discovery of two additional moons around Pluto, provisionally designated S/2005 P 1 (hereafter P1) and S/2005 P 2 (hereafter P2), which makes Pluto the first Kuiper belt object known to have multiple satellites. These new satellites are much smaller than Charon, with estimates of P1's diameter ranging from 60km to 165km, depending on the surface reflectivity; P2 is about 20 per cent smaller than P1. Although definitive orbits cannot be derived, both new satellites appear to be moving in circular orbits in the same orbital plane as Charon, with orbital periods of ~38 days (P1) and ~25 days (P2).