Program QUILF assesses equilibria among Ti-magnetite, ilmenite, augite, pigeonite, orthopyroxene, olivine, and quartz (or subassemblages thereof). Oxide and silicate equilibria are related through the QUIlF equilibrium: SiO2 + 2Fe2TiO4 = 2FeTiO3 + Fe2SiO4 Quartz Ulvospinel Ilmenite Fayalite. Depending on the assemblage, QUILF can provide information on temperature. pressure, oxygen fugacity, and the activities of SiO2, TiO2, and Fe-degrees at which the phases were last in equilibrium. For many low-variance assemblages, the system is overdetermined; thus quantitative information can be extracted even if one phase is altered or has reequilibrated. QUIlF equilibria can reduce the uncertainties in temperature and oxygen fugacity as determined from coexisting ilmenite and Ti-magnetite alone. QUILF is written in Turbo Pascal for IBM PC and compatibles. The compiled program is approximately 210 kbyte; it also requires two data files that total approximately 10 kbyte. The compositions of the phases first must be projected into seven-component space (CaO-MgO-MnO-FeO-Fe2O3-TiO2-SiO2) before they are used in program QUILF; routines to accomplish this are included in the program, and also are available as separate BASIC programs.