Cell-cycle progression requires careful regulation to ensure accurate propagation of genetic material to the daughter cells. Although many cell-cycle regulators are evolutionarily conserved in the protozoan parasite Trypanosoma brucei, novel regulatory mechanisms seem to have evolved. Here, we analyse the function of the histone methyltransferase DOT1A during cell-cycle progression. Over-expression of DOT1A generates a population of cells with aneuploid nuclei as well as enucleated cells. Detailed analysis shows that DOT1A over-expression causes continuous replication of the nuclear DNA. In contrast, depletion of DOT1A by RNAi abolishes replication but does not prevent karyokinesis. As histone H3K76 methylation has never been associated with replication control in eukaryotes before, we have discovered a novel function of DOT1 enzymes, which might not be unique to trypanosomes.