Linnaeus gave us the idea of systematics, with each taxon of lower rank nested inside one of higher rank; Darwin showed that these taxa are the result of evolution; Hennig demonstrated that, if they are to mean anything, all taxa must represent monophyla. He also proposed that, to bring objectivity into the system, each taxonomic rank should be characterised by a particular time depth, but this is not easy to bring about: genera such as Drosophila and Eucalyptus have a time-depth comparable to whole orders among mammals! Within restricted groups of organisms, however, time-depths do tend to vary within limits: we will not do too much violence to current usage if we insist that a modern mammal (including ruminant) genus must have a time-depth of about 5 million years, i.e. going back at least to the Miocene-Pliocene boundary, and a modern family must have a time-depth of about 25 million years, i.e. going back to the Oligocene-Miocene boundary. Molecular studies show that living ruminants present examples where the „traditional“ classification (in the main laid down in the mid-20th-century, and all too often still accepted as standard even today) violates Hennigian principles. Among Bovidae, the genera Bos, Tragelaphus, Gazella and Hemitragus are paraphyletic, and so, among Cervidae, are the genera Cervus and Mazama. I will discuss what we can do about these, and will then present, with commentary, a classification of living ruminants.