Eukaryotic cells have several quality control pathways that rely on translation to detect and degrade defective RNAs. Dom34 and Hbs1 are two proteins that are related to translation termination factors and are involved in no-go decay (NGD) and nonfunctional 18S ribosomal RNA (rRNA) decay (18S NRD) pathways that eliminate RNAs that cause strong ribosomal stalls. Here we present the structure of Hbs1 with and without GDP and a low-resolution model of the Dom34-Hbs1 complex. This complex mimics complexes of the elongation factor and transfer RNA or of the translation termination factors eRF1 and eRF3, supporting the idea that it binds to the ribosomal A-site. We show that nucleotide binding by Hbs1 is essential for NGD and 18S NRD. Mutations in Hbs1 that disrupted the interaction between Dom34 and Hbs1 strongly impaired NGD but had almost no effect on 18S NRD. Hence, NGD and 18S NRD could be genetically uncoupled, suggesting that mRNA and rRNA in a stalled translation complex may not always be degraded simultaneously.