Vocal mimicry provides a unique system for investigating song learning and cultural evolution in birds. Male lyrebirds produce complex vocal displays that include extensive and accurate mimicry of many other bird species. We recorded and analysed the songs of the Albert's lyrebird (Menura alberti) and its most commonly imitated model species, the satin bowerbird (Ptilonorhynchus violaceus), at six sites in southeast Queensland, Australia. We show that each population of lyrebirds faithfully reproduces the song of the local population of bowerbirds. Within a population, lyrebirds show less variation in song structure than the available variation in the songs of the models. These results provide the first quantitative evidence for dialect matching in the songs of two species that have no direct ecological relationship.