Ar-40/Ar-39 dating of fine-grained alunite that formed during cave genesis provides ages of formation for the Big Room level of Carlsbad Cavern [4.0 to 3.9 million years ago (Ma)], the upper level of Lechuguilla Cave (6.0 to 5.7 Ma), and three other hypogene caves (11.3 to 6.0 Ma) in the Guadalupe Mountains of New Mexico. Alunite ages increase and are strongly correlative with cave elevations, which indicates an 1100-meter decline in the water table, apparently related to tectonic uplift and tilting, from 11.3 Ma to the present. Ar-40/Ar-39 dating studies of the hypogene caves have the potential to help resolve late Cenozoic climatic, speleologic, and tectonic questions.