Based on electron microscopy, nonresonant microwave absorption, electron paramagnetic resonance, and other studies, it is shown that in the ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ system, compositions with \ensuremath{\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 \ensuremath{\delta}=0.3--0.4 region (${\mathit{T}}_{\mathit{c}}$\ensuremath{\sim}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 ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{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.