Thermogravimetric in situ measurements of oxygen loss from (RE)Ba2Cu3O6 samples (RE=Y, Nd, Er) heated isothermally in a relatively high dynamic vacuum were made with a Cahn RG electrobalance. Single-phase orthorhombic samples of composition (RE)Ba2Cu3O7-x (highest oxygen content) were synthesized from stoichiometric (1:2:3) mixtures of high-purity (RE)2O3, BaCO3 and CuO. The original 1:2:3 mixture was prepared by the two-stage procedure described earlier. The crystal structure of the sample in the original orthorhombic phase was controlled by the X-ray powder method (CuKα radiation) using a Stadi P Stoe diffractometer with a position-sensitive detector. The decomposition curves are described by the sum of exponential terms corresponding to rapid and slow first-order processes in which differently sized grains of the powder samples are involved. The activation energies are estimated from appropriate Arrhenius plots.