A Bahadur-Kiefer type process is formed by adding a process and its inverse. The classical process-inverse pairs are the uniform empirical-quantitle process and the partial sum-renewal process pairs. The first mentioned pair was first pointed out and investigated by Bahadur (1966) and Kiefer (1967, 1970). Vervaat (1972) was the first to identify the partial sum-renewal process pair as well as to study such pairs in general. The work of Paul Deheuvels and David Mason on this subject will be surveyed. It led to the first published proof of a difficult limit result stated without proof by Kiefer (1970) for the uniform empirical-quantitle process pair.
