Apophyllite (KCa4Si8O20(F, OH)⋅8H2O), which formed as a low-temperature secondary mineral in the Kirkpatrick Basalt, has been examined to evaluate its potential for geochronology using the K-Ar (by the 40Ar/39Ar technique) and Rb-Sr methods. The 40Ar/39Ar total-gas ages for apophyllites from the Kirkpatrick Basalt are 114--133 Ma for the central Transantarctic Mountains, 95--114 Ma for south Victoria Land, and 76--100 Ma for north Victoria Land. Within individual hand samples, apophyllite 40Ar/39Ar apparent ages show variations of up to 24 m.y., and within single large (up to ~2 cm) crystals, differences of up to 14 m.y. are observed. The 40Ar/39Ar incremental-heating spectra are generally flat but have low- and high-temperature discordances attributed to 39Ar recoil. Rb-Sr model ages for the apophyllites range from 94 to 144 Ma and vary from concordant with the 40Ar/39Ar dates to as much as 14 m.y. older. The dates are consistent with other temporal indicators of low-temperature alteration in the basalts and are interpreted to broadly reflect the time of apophyllite precipitation. They document a geographically widespread early to middle Cretaceous secondary mineralization which is inferred to be caused by a major period of ground-water movement associated with the initiation of uplift and denudation of the Transantarctic Mountains. The results suggest that apophyllite can produce geologically meaningful ages by both Rb-Sr and K-Ar methods, although further work is required to fully understand the variations in age that may be attributed to Ar loss, alkali mobility, or an extended history of mineral precipitation. ¿ 1999 American Geophysical Union