Acid phosphatase (AP) is readily inactivated when exposed to the free radicals generated in the pyrolysis of 2,2′-azobis(2-amidinopropane) hydrochloride (AAPH) under aerobic conditions. On average, a large number of tryptophan groups are modified by each protein molecule that loses its catalytic activity. In spite of this, the enzyme inactivation takes place without induction times, a result that indicates either that damage is progressive or that damage of a critical target is needed to inactivate the enzyme (all-or-nothing mechanism). A Lineweaver–Burk plot of the enzyme activity measured at pH 4.8 is not compatible with an all-or-nothing mechanism, showing that after exposure of the native protein ensemble to the free radical source there are partially damaged molecules whose affinity for the substrate is widely different from that of the native molecules. On the other hand, the partially damaged ensemble shows a normal Michaelis–Menten behavior when the activity is measured at pH 7.0, with only a reduced value of VM, relative to that of the unmodified ensemble. These results show that the native protein and modified proteins that remain active constitute different populations, with different responses to pH changes. Comparative heat denaturation studies of the native and pretreated proteins support this proposal.