The RecQ DNA helicases human BLM and yeast Sgs1 interact with DNA topoisomerase III and are thought to act on stalled replication forks to maintain genome stability. To gain insight into this mechanism, we previously identified SLX1 and SLX4 as genes that are required for viability and for completion of rDNA replication in the absence of SGS1-TOP3. Here we show that SLX1 and SLX4 encode a heteromeric structure-specific endonuclease. The Slx1-Slx4 nuclease is active on branched DNA substrates, particularly simple-Y, 5'-flap, or replication fork structures. It cleaves the strand bearing the 5' nonhomologous arm at the branch junction and generates ligatable nicked products from 5'-flap or replication fork substrates. Slx1 is the founding member of a family of proteins with a predicted URI nuclease domain and PHD-type zinc finger. This subunit displays weak structure-specific endonuclease activity on its own, is stimulated 500-fold by Slx4, and requires the PHD finger for activity in vitro and in vivo. Both subunits are required in vivo for resistance to DNA damage by methylmethane sulfonate (MMS). We propose that Sgs1-Top3 acts at the termination of rDNA replication to decatenate stalled forks, and, in its absence, Slx1-Slx4 cleaves these stalled forks.