The U-Pb isotope systematics of uraniferous opals from Spor Mountain, Utah, were investigated to determine the suitability of such material for geochronologic purposes, and to estimate the timing of uranium and associated beryllium and fluorine mineralization. The results indicate that uraniferous opals can approximate a closed system for uranium and uranium daughters, so that dating samples as young as ???1 m.y. should be possible. In addition, the expected lack of initial 230Th and 231Pa in opals permits valuable information on the initial 234U/238U to be obtained on suitable samples of ???10 m.y. age. The oldest 207Pb/235U apparent age observed, 20.8 ?? 1 m.y., was that of the opal-fluorite core of a nodule from a beryllium deposit in the Spor Mountain Formation. This age is indistinguishable from that of fission-track and K-Ar ages from the host rhyolite, and links the mineralization to the first episode of alkali rhyolite magmatism and related hydrothermal activity at Spor Mountain. Successively younger ages of 13 m.y. and 8-9 m.y. on concentric outer zones of the same nodule indicate that opal formed either episodically or continuously for over 10 m.y. Several samples of both fracture-filling and massive-nodule opal associated with beryllium deposits gave 207Pb/235U apparent ages of 13-16 m.y., which may reflect a restricted period of mineralization or perhaps an averaging of 21- and <13-m.y. periods of opal growth. Several samples of fracture-filling opal in volcanic rocks as young as 6 m.y. gave 207Pb/235U ages of 3.4-4.8 m.y. These ages may reflect hot-spring activity after the last major eruption of alkali rhyolite. ?? 1980.