A ubiquitin ligase complex found to be involved in post-replicative bypass of UV-damaged DNA and UV mutagenesis. In S. cerevisiae, the complex contains the ubiquitin conjugating enzyme Rad6 and Rad18, a protein containing a RING finger motif and a nucleotide binding motif. The yeast Rad6-Rad18 heterodimer has ubiquitin conjugating activity, binds single-stranded DNA, and possesses single-stranded DNA-dependent ATPase activity.