We investigated the tempo and mode of evolution of the primate T-lymphotropic viruses (PTLVs). Several different models of nucleotide substitution were tested on a general phylogenetic tree obtained using the 20 full-genome HTLV/STLV sequences available. The likelihood ratio test showed that the Tamura and Nei model with discrete gamma-distributed rates among sites is the best-fitting substitution model. The heterogeneity of nucleotide substitution rates along the PTLV genome was further investigated for different genes and at different codon positions (cdp's). Tests of rate constancy showed that different PTLV lineages evolve at different rates when first and second cdp's are considered, but the molecular-clock hypothesis holds for some PTLV lineages when the third cdp is used. Negative selection was evident throughout the genome. However, in the gp46 region, a small fragment subjected to positive selection was identified using a Monte Carlo simulation based on a likelihood method. Employing correlations of the virus divergence times with anthropologically documented migrations of their host, a possible timescale was estimated for each important node of the PTLV tree. The obtained results on these slow-evolving viruses could be used to fill gaps in the historical records of some of the host species. In particular, the HTLV-I/STLV-I history might suggest a simian migration from Asia to Africa not much earlier than 19,500-60,000 years ago.