The incident energy dependence of recoil ranges of P32, S35, Ar38, and Ar39 formed in thorium and uranium by 0.6-24 GeV protons has been studied by the thick-target-thick-catcher technique. While the range of Ar38 and Ar39 produced in thorium decreases noticeably between 1 and 24 GeV, that of P32 produced in the same target decreases slightly between 0.6 and 21 GeV. The constancy of range over this energy interval is interpreted as fragmentation, while a marked decrease is considered to be characteristic of deep spallation. Fragmentation and deep spallation are interpreted as collective interaction mechanisms, for which the role of the impact parameter of the initial collision (proton-target nucleus) is emphasized. NUCLEAR REACTIONS Measurement of 2W(F+B) of P32, S35, Ar38, and Ar39 formed in thorium and uranium by 0.6-24 GeV protons.