The 26S proteasome has a highly complicated structure comprising the 20S core particle (CP) and the 19S regulatory particle (RP). Along with the standard CP in all eukaryotes, vertebrates have two more subtypes of CP called the immunoproteasome and the thymoproteasome. The immunoproteasome has catalytic subunits β1i, β2i, and β5i replacing β1, β2, and β5 and enhances production of major histocompatibility complex I ligands. The thymoproteasome contains thymus-specific subunit β5t in place of β5 or β5i and plays a pivotal role in positive selection of CD8+ T cells. Here we investigate the assembly pathways of the specialized CPs and show that β1i and β2i are incorporated ahead of all the other β-subunits and that both β5i and β5t can be incorporated immediately after the assembly of β3 in the absence of β4, distinct from the assembly of the standard CP in which β-subunits are incorporated in the order of β2, β3, β4, β5, β6, β1, and β7. The propeptide of β5t is a key factor for this earlier incorporation, whereas the body sequence seems to be important for the earlier incorporation of β5i. This unique feature of β5t and β5i may account for preferential assembly of the immunoproteasome and the thymoproteasome over the standard type even when both the standard and specialized subunits are co-expressed.