A great number of pure and homogeneous Y2Ba4Cu7Oz samples were investigated by AC susceptibility, field cooling magnetization measurements, X-ray diffraction, microprobe analysis and microstructural examinations in a light microscope and a scanning electron microscope. The oxygen content z between 14.1 and 15.3 was determined by the reduction of the samples in a hydrogen flow. To reach the (z-T-p) equilibrium, well-crystallized samples were annealed in pure oxygen (10−6 ⩽p(O2)⩽102 bar) between 300 and 900°C and subsequently quenched. The specimens produced in this way show sharp χAC transitions in the entire range of critical temperatures (30 K ⩽ Tc ⩽ 95 K). The correlation Tc versus the orthorhombicity 2(b−a)/(b+a) is almost linear, similar to that observed in YBa2Cu3Ox. This is contrast to the distinct behaviour of the functions Tc versus z and Tc versus x in these two compounds. We present a stability-decomposition map 0for Y2Ba4Cu7Oz over a wide range of (T, p) coordinates.