The yeast nuclear exosome contains multiple 3'-->5' exoribonucleases, raising the question of why so many activities are present in the complex. All components are required during the 3' processing of the 5.8S rRNA, together with the putative RNA helicase Dob1p/Mtr4p. During this processing three distinct steps can be resolved, and hand-over between different exonucleases appears to occur at least twice. 3' processing of snoRNAs (small nucleolar RNAs) that are excised from polycistronic precursors or from mRNA introns is also a multi-step process that involves the exosome, with final trimming specifically dependent on the Rrp6p component. The spliceosomal U4 snRNA (small nuclear RNA) is synthesized from a 3' extended precursor that is cleaved by Rnt1p at sites 135 and 169 nt downstream of the mature 3' end. This cleavage is followed by 3'-->5' processing of the pre-snRNA involving the exosome complex and Dob1p. The exosome, together with Rnt1p, also participates in the 3' processing of the U1 and U5 snRNAs. We conclude that the exosome is involved in the processing of many RNA substrates and that different components can have distinct functions.