The proteasome is responsible for selective degradation of proteins. It exists in mammalian cells under four main subtypes, which differ by the combination of their catalytic subunits: the standard proteasome (β1-β2-β5), the immunoproteasome (β1i-β2i-β5i) and the two intermediate proteasomes (β1-β2-β5i and β1i-β2-β5i). The efficiency of the four proteasome subtypes to degrade ubiquitinated or oxidized proteins remains unclear. Using cells expressing exclusively one proteasome subtype, we observed that ubiquitinated p21 and c--myc were degraded at similar rates, indicating that the four 26S proteasomes degrade ubiquitinated proteins equally well. Under oxidative stress, we observed a partial dissociation of 26S into 20S proteasomes, which can degrade non-ubiquitinated oxidized proteins. Oxidized calmodulin and hemoglobin were best degraded in vitro by the three β5i-containing 20S proteasomes, while their native forms were not degraded. Circular dichroism analyses indicated that ubiquitin-independent recognition of oxidized proteins by 20S proteasomes was triggered by the disruption of their structure. Accordingly, β5i-containing 20S proteasomes degraded unoxidized naturally disordered protein tau, while 26S proteasomes did not. Our results suggest that the three β5i-containing 20S proteasomes, namely the immunoproteasome and the two intermediate proteasomes, might help cells to eliminate proteins containing disordered domains, including those induced by oxidative stress.