The magnetic properties of bimagnetic core/shell nanoparticles consisting of an antiferromagnetic MnO core and a ferrimagnetic passivation shell have been investigated. It is found that the phase of the passivation shell (gamma-Mn(2)O(3) or Mn(3)O(4)) depends on the size of the nanoparticles. Structural and magnetic characterizations concur that while the smallest nanoparticles have a predominantly gamma-Mn(2)O(3) shell, larger ones have increasing amounts of Mn(3)O(4). A considerable enhancement of the Néel temperature, T(N), and the magnetic anisotropy of the MnO core for decreasing core sizes has been observed. The size reduction also leads to other phenomena such as persistent magnetic moment in MnO up to high temperatures and an unusual temperature behavior of the magnetic domains.