Degradation of a protein by the ubiquitin-proteasome system (UPS) is a multistep process catalyzed by sequential reactions. Initially, ubiquitin is conjugated to the substrate in a process mediated by concerted activity of three enzymes; the last of them-a ubiquitin ligase (E3)-belongs to a family of several hundred members, each recognizing a few specific substrates. This is followed by repeated addition of ubiquitin moieties to the previously conjugated one to generate a ubiquitin chain that serves as a recognition element for the proteasome, which then degrades the substrate. Ubiquitin is recycled via the activity of deubiquitinating enzymes (DUBs). It stands to reason that efficiency of such a complex process would depend on colocalization of the different components in an assembly that allows the reactions to be carried out sequentially and processively. Here we describe nuclear condensates that are dynamic in their composition. They contain p62 as an essential component. These assemblies are generated by liquid-liquid phase separation (LLPS) and also contain ubiquitinated targets, 26S proteasome, the three conjugating enzymes, and DUBs. Under basal conditions, they serve as efficient centers for proteolysis of nuclear proteins (e.g., c-Myc) and unassembled subunits of the proteasome, suggesting they are involved in cellular protein quality control. Supporting this notion is the finding that such foci are also involved in degradation of misfolded proteins induced by heat and oxidative stresses, following recruitment of heat shock proteins and their associated ubiquitin ligase CHIP.