Phase equilibria of the ZnO-SiO2, Al2O3-SiO2 and ZnO-Al2O3-SiO2 systems at liquidus were characterized at 1340-1740 degrees C in air. The ZnO-Al2O3 subsolidus phase equilibria were derived from the experiments with the SiO2- and CaO + SiO2-containing slags. High-temperature equilibration on silica or platinum substrates, followed by quenching and direct measurement of Zn, Al, Si and Ca concentrations in the phases with the electron probe X-ray microanalysis (EPMA) was used to accurately characterize the system. Special attention was given to zincite phase that was shown to consist of two separate ranges of compositions: round-shaped low-Al zincite (<2 mol.% AlO1.5) and platy high-Al zincite (4-11 mol.% AlO1.5). A technique was developed for more accurate measurement of the ZnO solubility in the low-ZnO phases (corundum, mullite, tridymite and cristobalite) surrounded by the ZnO-containing slag, using L-line for Zn instead of K-line, avoiding the interference of secondary X-ray fluorescence. Solubility of ZnO was found to be below 0.03 mol.% in corundum and cristobalite, and below 0.3 mol.% in mullite. Present experimental data were used to obtain a self-consistent set of parameters of the thermodynamic models for all phases in this system using FactSage computer package. The modified quasichemical model with two sublattices (Zn2+, Al3+, Si4+) (O2- ) was used for the liquid slag phase; the compound energy formalism was used for the spinel (Zn2+,Al3+)[Zn2+,Al3+,Va]2O2-4 and mullite Al3+2(Al3+,Si4+) (O2-,Va)5 phases; the Bragg-Williams formalism was used for the zincite (ZnO, Al2O3); other solid phases (tridymite and cristobalite SiO2, corundum Al2O3, and willemite Zn2SiO4) were described as stoichiometric. Present study is a part of the research program on the characterization of the multicomponent Pb-Zn-Cu-Fe-Ca-Si-O-S-Al-Mg-Cr-As-Sn-Sb-Bi-Ag-Au-Ni system.