Abstract. Given a phylogenetic tree T for a family of tandemly repeated genes and their signed order O on the chromosome, we aim to find the minimum number of inversions compatible with an evolutionary history of this family. This is the first attempt to account for inversions in an evolutionary model of tandemly repeated genes. We present a time-efficient branch-and-bound algorithm and show, using simulated data, that it can be used to detect "wrong" phylogenies among a set of putative ones for a given gene family. An application on a published phylogeny of KRAB zinc finger genes is presented. Key words: gene family, gene order, inversion, duplication, phylogeny