Based on electron microscopy, nonresonant microwave absorption, electron paramagnetic resonance, and other studies, it is shown that in the YBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}} system, compositions with {delta}=0.0--0.20, 0.25, and 0.5 are stable and monophasic, the last two being associated with ordered-oxygen-vacancy structures. The {delta}=0.3--0.4 region ({ital T}{sub {ital c}}{approximately}60 K) is not associated with an ordered-vacancy structure. More importantly, compositions in this region undergo structural changes on annealing at relatively low tempertures, eventually decomposing to the more stable phases. It appears that compositions such as YBa{sub 2}Cu{sub 3}O{sub 6.7} are not thermodynamically stable, casting thereby some doubt on the belief that the 60-K regime represents a genuine single-phase superconducting material.