There is widespread photogeological evidence for ubiquitous water flowing on the surface of Mars. However, the age of surface and near-surface water cannot be deduced with high precision from photogeology. While there is clear evidence for old and young fluvial features in the photogeologic record, the uncertainty in the absolute calibration of the Martian crater flux results in uncertainties of ¿1.5 Gyr in the middle period of Martian geologic history. Aqueous alteration of primary igneous minerals produces secondary minerals in Martian meteorites. Here we use the ages of secondary alteration minerals in Martian meteorites to obtain absolute ages when liquid water was at or near the surface of Mars. Aqueous alteration events in Martian meteorites occurred at 3929 ¿ 37 Ma (carbonates in ALH84001), 633 ¿ 23 Ma (iddingsite in nakhlites), and 0--170 Ma (salts in shergottites). Furthermore, these events appear to be of short duration, suggesting episodic rather than continuous aqueous alteration of the meteorites. The Martian meteorites appear to be contaminated by Martian surface Pb characterized by a 207Pb/206Pb ratio near 1. Lead of this composition could be produced by water-based alteration on the Martian surface. The high 129Xe/132Xe ratio in the Martian atmosphere compared to Martian meteorites indicates fractionation of I from Xe within ~100 Myr after nucleosynthesis of 129I. Such fractionation is difficult to achieve through magmatic processes. However, water very efficiently fractionates I from Xe, raising the intriguing possibility that Mars had a liquid water ocean within its first 100 Myr.1.