Proteolysis is essential for the execution of many cellular functions. These include removal of incorrectly folded or damaged proteins(1), the activation of transcription factors(2), the ordered degradation of proteins involved in cell cycle control(3), and the generation of peptides destined for presentation by class I molecules of the major histocompatibility complex(4). A multisubunit protease complex, the proteasome(5), accomplishes these tasks. Here we show that in mammalian cells inactivation of the proteasome by covalent inhibitors allows the outgrowth of inhibitor-resistant cells. The growth of such adapted cells is apparently maintained by the induction of other proteolytic systems that compensate for the loss of proteasomal activity.