In a recent study, Hardy et al. (2012) examined ten samples of dental calculus from five Neanderthal individuals from El Sidrón in northern Spain (occupation dates between 47300 and 50600 BP). In calculus from a young adult, they discovered the presence of compounds (dihydroazulene, chamazulene and methylherniarin) that occur in yarrow (Achillea millefolium) and camomile (Matriarca chamomilla). In preference to other hypotheses, the authors proposed that these two plants were used for self-medication. In this paper, we do not reject the self-medication hypothesis, but our observations of wild chimpanzees in Uganda, at Sonso in the Budongo Forest Reserve and at Kanyawara and Sebitoli in Kibale National Park (separated by about 150km), as well as ethnological and palaeontological evidence, lead us to propose three other explanations for the presence of these compounds. In addition, data on Neanderthal behaviour suggest that their subsistence and technological strategies were complex.