R-loops are stable RNA-DNA hybrids that have been implicated in transcription initiation and termination, as well as in telomere homeostasis, chromatin formation, and genome replication and instability. RNA Polymerase (Pol) II transcription in the protozoan parasite Trypanosoma brucei is highly unusual: virtually all genes are co-transcribed from multigene transcription units, with mRNAs generated by linked transsplicing and polyadenylation, and transcription initiation sites display no conserved promoter motifs. Here, we describe the genome-wide distribution of R-loops in wild type mammal-infective T. brucei and in mutants lacking RNase H1, revealing both conserved and diverged functions. Conserved localisation was found at centromeres, rRNA genes and retrotransposon-associated genes. RNA Pol II transcription initiation sites also displayed R-loops, suggesting a broadly conserved role despite the lack of promoter conservation or transcription initiation regulation. However, the most abundant sites of R-loop enrichment were within the intergenic regions of the multigene transcription units, where the hybrids coincide with sites of polyadenylation and nucleosome-depletion. Thus, instead of functioning in transcription termination, most T. brucei R-loops act in a novel role, promoting RNA Pol II movement or mRNA processing. Finally, we show there is little evidence for correlation between R-loop localisation and mapped sites of DNA replication initiation.