Abstract For convenience, we treat all “polyneopteran” orders together. Five orders of hemimetabolous “Polyneoptera” include species alien to Europe, namely Blattodea, Isoptera, Orthoptera, Phasmatodea and Dermaptera. A total of 37 species alien to Europe have been recorded. These belong to 14 different families. Most of these species show a detritivorous feeding regime (22 spp.), whereas 12 species are phytophagous and two are predators. The majority of species were first observed between 1900 and 1975. Unlike other arthropod groups, the mean number of polyneopteran species newly recorded per year showed no acceleration since 1975. The alien “Polyneoptera” mostly originated from Central/South America and Asia (10 species each, 27.0%), followed by Africa (7, 18.9%). Germany hosts the largest number of alien Polyneoptera (15 spp.), followed by Denmark (14), Spain (11) and France (10). All but one alien species represent unintentional introductions. More than 75% of the species are associated with artificial habitats (houses, buildings and greenhouses) and cultivated areas. Blattodea and Isoptera have huge economic and/or medical importance. The cost of treatments and sanitary measures against termites and cockroaches, in particular, is significant in Europe.