Retrotransposons are ubiquitous mobile genetic elements that have played a significant role in shaping eukaryotic genome evolution. The genome of the yeast Saccharomyces cerevisiae harbours five families of retrotransposons, Ty1-Ty5. With the publication of the S. cerevisiae genome sequence, for the first time a full genomic complement of retrotransposon sequences is available. Analysis of these sequences promises to yield insight into the nature of host--transposon coevolution. Evolutionary change in Ty elements depends on their replication and excision rates, which have been determined in the laboratory. Rates measured in the laboratory may differ from those that have operated over evolutionary time. Based on an analysis of sequence data for the Ty1, Ty2 and hybrid Ty1/2 families, we develop a novel 'genomic demography' model to estimate long-term transposition and excision rates and to estimate how long ago these elements entered the yeast genome. We find that rates of excision and transposition have averaged 7.2-8.7 x 10(-8) per generation over evolutionary time. Two separate models provide upper- and lower-bound estimates for the age of the system, suggesting that the first elements entered the genome between approximately 50 million and 250 million generations ago.