In contrast to ordinary ferroelectrics where the temperature T m of the permittivity maximum monotonically increases with bias field E in ͑1−x͒PbMg 1/3 Nb 2/3 O 3 -͑x͒PbTiO 3 ͑0 ഛ x ഛ 0.35͒ single crystals, T m was found to remain constant or to decrease with E up to a certain threshold field E t , above which T m starts increasing. The threshold field E t decreases with increasing x, tending toward zero at approximately x = 0.4. We explain this dependence in the framework of models which take into account quenched random fields and random bonds. For crystals with 0.06ഛ x ഛ 0.13, the E-T phase diagrams are constructed. In contrast to PMN, they exhibit an additional, nearly field-independent boundary, in the vicinity of the Vogel-Fulcher temperature. We believe this boundary to correspond to an additional phase transition and the appearing order parameter is likely to be nonpolar.