Invasive species are classically thought to suffer from reduced within-population genetic variation compared to their native-range sources due to founder effects and population bottlenecks during introduction. Reduction in genetic variation in introduced species may limit population growth, increase the risk of extinction, and constrain adaptation, hindering the successful establishment and spread of an alien species. Results of recent empirical studies, however, show higher than expected genetic variation, rapid evolution, and multiple native-range sources in introduced populations, which challenge the classical scenario of invasive-species genetics. With mitochondrial DNA (mtDNA) sequence data, we examined the molecular genetics of 10 replicate introductions of 8 species of Anolis lizards. Eighty percent of introductions to Florida and the Dominican Republic were from multiple native-range source populations. MtDNA haplotypes restricted to different geographically distinct populations in the native range of a species commonly occurred as intrapopulation polymorphisms in introduced populations. Two-thirds of introduced populations had two or more sources, and admixture elevated genetic variation in half of the introduced populations above levels typical of native-range populations. The mean pairwise sequence divergence among haplotypes sampled within introduced populations was nearly twice that within native-range populations (2.6% vs. 1.4%). The dynamics of introductions from multiple sources and admixture explained the observed genetic contrasts between native and introduced Anolis populations better than the classical scenario for most introduced populations. Elevated genetic variation through admixture occurred regardless of the mode or circumstances of an introduction. Little insight into the number of sources or amount of genetic variation in introduced populations was gained by knowing the number of physical introductions, the size of a species' non-native range, or whether it was a deliberate or accidental introduction. We hypothesize that elevated genetic variation through admixture of multiple sources is more common in biological invasions than previously thought. We propose that introductions follow a sequential, two-step process involving a reduction in genetic variation due to founder effects and population bottlenecks followed by an increase in genetic variation if admixture of individuals from multiple native-range sources occurs.