Human African Trypanosomiasis (HAT, sleeping sickness) and Animal African Trypanosomiasis (AAT) are neglected tropical diseases generally caused by the same etiological agent, Trypanosoma brucei. Despite important advances in the reduction or disappearance of HAT cases, AAT represents a risky reservoir of the infections. There is a strong need to control AAT, as is claimed by the European Commission in a recent document on the reservation of antimicrobials for human use. Control of AAT is considered part of the One Health approach established by the FAO program against African Trypanosomiasis. Under the umbrella of the One Health concepts, in this work, by analyzing the pharmacological properties of the therapeutic options against Trypanosoma brucei spp., we underline the need for clearer and more defined guidelines in the employment of drugs designed for HAT and AAT. Essential requirements are addressed to meet the challenge of drug use and drug resistance development. This approach shall avoid inter-species cross-resistance phenomena and retain drugs therapeutic activity.