Solubilities of accessory minerals (apatite, monazite, zircon and rutile) in supercritical aqueous fluids have been measured to evaluate the role of these fluids in the mobilization of accessory mineral-hosted trace elements. We have characterized the effects on solubility of pH, X(H2O) (addition of CO2), pressure (P = 1.0-3.0 GPa), temperature (T = 800-1200-degrees-C), and dissolved silicate and NaCl concentration. Fluorapatite solubility in pure H2O is low, not more than 0.4 wt% at all conditions studied, but increases strongly with decreasing pH. Changes in P, T, X(H2O), M(NaCl) (the molality of NaCl), and dissolved silicate concentration have comparatively little effect on apatite solubility. Monazite is even less soluble in H2O (not more than 0.2 wt%). Limited data suggests that monazite solubility increases with increasing P and T and with decreasing pH, but is insensitive to M(NaCl). Zircon reacts with H2O to form baddeleyite (ZrO2) + silica-rich fluid. ZrO2 solubility in H2O and 1 M HCl is less than 0.2 wt%. Zircon, and therefore ZrO2, solubility in quartz-saturated fluids +/- HCl +/- NaCl and in H2O-CO2 fluids is also very low. Rutile is more soluble than the other minerals examined, in the wt% range, and its solubility increases with increasing P and T. Results indicate that high P-T aqueous fluids can dissolve significant amounts of Ti but very little Zr, and little phosphate unless the fluids are acidic. In most cases, apatite, monazite and zircon will remain present during episodes of aqueous fluid metasomatism and therefore will exert control, as 'residual phases', over element distribution. The higher solubility of rutile relative to other accessory minerals at high pressure may result in the depletion of high field strength elements relative to large ion lithophile elements observed in subduction zone volcanics.