We report a μSR study of four EuBa 2 Cu 3 O 6 + x samples prepared with different oxygen stoichiometry (x=0.25-0.5) and annealing temperatures. In all the samples except the least-doped one, the high-T N antiferromagnetic phase was found to coexist with a sizable non-magnetic fraction which, in the x>=0.38 samples annealed at a higher temperature, develops superconductivity with a surprisingly high T c =93K. Complementary Cu-NQR investigation rules out trivial chemical inhomogeneities as the origin of the phase-separated state, and rather points to intrinsic phase separation mechanisms, such as stripe-phase instabilities.