Trypanosoma brucei is a kinetoplastid flagellate, the agent of human sleeping sickness and ruminant nagana in Africa. Kinetoplastid flagellates contain their eponym kinetoplast DNA (kDNA), consisting of two types of interlocked circular DNA molecules: scores of maxicircles and thousands of minicircles. Maxicircles have typical mitochondrial genes, most of which are translatable only after RNA editing. Minicircles encode guide RNAs, required for decrypting the maxicircle transcripts. The life cycle of T. brucei involves a bloodstream stage (BS) in vertebrates and a procyclic stage (PS) in the tsetse fly vector. Partial [dyskinetoplastidy (Dk)] or total [akinetoplastidy (Ak)] loss of kDNA locks the trypanosome in the BS form. Transmission between vertebrates becomes mechanical without PS and tsetse mediation, allowing the parasite to spread outside the African tsetse belt. Trypanosoma equiperdum and Trypanosoma evansi are agents of dourine and surra, diseases of horses, camels, and water buffaloes. We have characterized representative strains of T. equiperdum and T. evansi by numerous molecular and classical parasitological approaches. We show that both species are actually strains of T. brucei, which lost part (Dk) or all (Ak) of their kDNA. These trypanosomes are not monophyletic clades and do not qualify for species status. They should be considered two subspecies, respectively T. brucei equiperdum and T. brucei evansi, which spontaneously arose recently. Dk/Ak trypanosomes may potentially emerge repeatedly from T. brucei.