In this paper we employ recently developed statistical and molecular tools to analyse the population history of the Tanzanian leopard (Panthera pardus), a large solitary felid. Because of their solitary lifestyle little is known of their past or present population dynamics. Eighty-one individuals were scored at 18 microsatellite loci. Overall, levels of heterozygosity were high (0.77 ± 0.03), with a small heterozygote deficiency (0.06 ± 0.03). Effective population size (Ne) was calculated to be 38 000–48 000. A Ne:N ratio of 0.42 (average from four cat studies) gives a present population size of about 100 000 leopards in Tanzania. Four different bottleneck tests indicated that this population has been large and stable for a minimum of several thousand years. FST values were low and no significant genetic structuring of the population could be detected. This concurs well with the large migration values (Nm) obtained (>3.3 individuals/generation). Our analysis reveals that ecological factors (e.g. disease), which are known to have had major impact on other carnivore populations, are unlikely to have impacted strongly on the population dynamics of Tanzanian leopards. The explanation may be found in their solitary life-style, their often nonconfrontational behaviour toward interspecific competitors, or that any bottlenecks have been of limited size, localized, or too short to have affected genetic variation to any measurable degree. Since the genetic structuring is weak, gene flow is not restricted to within protected areas. Local loss of genetic variation is therefore not of immediate concern.