Population genetic methods are widely used to retrace the introduction routes of invasive species. The unsupervised Bayesian clustering algorithm implemented in STRUCTURE is amongst the most frequently use of these methods, but its ability to provide reliable information about introduction routes has never before been assessed. We used computer simulations of microsatellite datasets to evaluate the extent to which the clustering results provided by STRUCTURE were misleading for the inference of introduction routes for two invasive populations independently introduced from a native population. For this simple scenario of independent introductions, the assumption of two clusters (i.e. K=2) would not be expected to result in STRUCTURE assigning the native population to one cluster, with both invasive populations assigned to the second cluster. We investigated the influence of two demographic parameters (effective size and bottleneck severity) and different numbers of loci on the type and frequency of misleading results. We showed that misleading STRUCTURE results were obtained for 10% of our simulated datasets and at a frequency of up to 37% for some combinations of parameters. Our results highlighted two different categories of misleading output. The first occurs in situations in which the native population has a low level of diversity. In this case, the two introduced populations may be very similar, despite their independent introduction histories. The second category results from convergence issues in STRUCTURE for K=2, with strong bottleneck severity and/or large numbers of loci resulting in high levels of differentiation between the three populations.