High-Tc GdBa2Cu3O7−δ superconductor bolometers with operation temperatures near 89 K, large receiving areas of 0.95 mm2 and very high detectivity have been made. The bolometers are supported by 0.62 μm thick silicon nitride membranes. A specially developed silicon-on-nitride layer was used to enable the epitaxial growth of the high-Tc superconductor. Using a gold black absorption layer an absorption efficiency for wavelengths between 70 and 200 μm of about 83% has been established. The noise of the best devices is fully dominated by the intrinsic phonon noise of the thermal conductance G,G, and not by the 1/f1/f noise of the superconducting film. The temperature dependence of the noise and the resulting optimum bias temperature have been investigated. In the analysis the often neglected effect of electrothermal feedback has been taken into account. The minimum electrical noise equivalent power (NEP) of a bolometer with a time constant τ of 95 ms is 2.9 pW/Hz1/2 which corresponds with an electrical detectivity D* of 3.4×1010 cm Hz1/2/W. Similar bolometers with τ=27 ms and NEP=3.8 pW/Hz1/2 were also made. No degradation of the bolometers could be observed after vibration tests, thermal cycling and half a year storage. Measurements of the noise of a Pr doped YBa2Cu3O7−δ film with Tc=40 K show that with such films the performance of air bridge type high-Tc bolometers could be improved.