Introgression, the incorporation of foreign variants through hybridization and repeated backcross, is increasingly being studied for its potential evolutionary consequences, one of which is adaptive introgression (AI). In recent years, several statistical methods have been proposed for the detection of loci that have undergone adaptive introgression. Most of these methods have been tested and developed to infer the presence of Neanderthal or Denisovan AI in humans. Currently, the behaviour of these methods when faced with genomic datasets from evolutionary scenarios other than the human lineage remains unknown. This study therefore focuses on testing the performance of the methods using test data sets simulated under various evolutionary scenarios inspired by the evolutionary history of human, wall lizard (Podarcis) and bear (Ursus) lineages. These lineages were chosen to represent di[ff]erent combinations of divergence and migration times. We study the impact of these parameters, as well as migration rate, population size, selection coefficient and presence of recombination hotspots, on the performance of three methods (VolcanoFinder, Genomatnn and MaLAdapt) and a standalone summary statistic (Q95(w, y)). Furthermore, the hitchhiking e[ff]ect of an adaptively introgressed mutation can have a strong impact on the [fl]anking regions, and therefore on the discrimination between the genomic windows classes (i.e. AI/non-AI). For this reason, three di[ff]erent types of non-AI windows are taken into account in our analyses: independently simulated neutral introgression windows, windows adjacent to the window under AI, and windows coming from a second neutral chromosome unlinked to the chromosome under AI. Our results highlight the importance of taking into account adjacent windows in the training data in order to correctly identify the window with the mutation under AI. Finally, our tests show that methods based on Q95 seem to be the most e[ffi]cient for an exploratory study of AI.