  We performed zero and transverse field MuSR experiments on a large number of
YBa2Cu3O6+x samples. We detect coexistence of antiferro-type (AF) short range
magnetism with superconductivity below T_f~10 K in compositions 0.37<x<0.39.
Most muons experience local AF fields, even when SQUID detects a full SC volume
fraction, which points to a local minimal interference organization of short AF
stripes embedded in the superconductor. A detailed phase diagram is produced
and the consequences of the minimal interference are discussed.
