The following main results are presented: • a critical assessment of the available thermodynamic data from different experiments for two solid solutions, YBa 2Cu 3O 6+ z (0 ⩽ z ⩽ 1) and Y 2Ba 4Cu 7O 14+ w (0 ⩽ w ⩽ 1), and for one stoichiometric compound YBa 2Cu 4O 8; • an analytical representation of the Gibbs energy functions for these phases; • a computer-assisted optimization analysis to obtain model parameters which best fit experimental data and are consistent with thermodynamic relations. The conditions for the existence of the other ordered superconducting phase, which can be formed as a stable superstructure of the YBa 2Cu 3O 6+ z phase are also outlined. More than 3500 experimental points obtained in a variety of experiments published in 110 papers have been processed in order to obtain the most reliable thermodynamic functions of phases over the temperature range from 250 to 1300 K and at pressures up to 100 kbar. The models with four sublattices were developed to describe the properties of the YBa 2Cu 3O 6+ z and Y 2Ba 4Cu 7O 14+ w solid solutions. For the former solution, the model and the optimization procedure based on the maximum likelihood method with the linear error model is described in detail earlier.