Tandemly arrayed genes (TAG) constitute a large fraction of most genomes and play important biological roles. They evolve through unequal recombination, which places duplicated genes next to the original ones (tandem duplications). Many algorithms have been proposed to infer a tandem duplication history for a TAG cluster in a single species. However, the presence of different transcriptional orientations in most TAG clusters highlight the fact that processes such as inversions also contribute to their evolution. This makes those algorithms unsuitable in many cases. To circumvent this limitation, we proposed in a previous work an extended evolutionary model which includes inversions and presented a branch-and-bound algorithm allowing to infer a most parsimonious scenario of evolution for a given TAG cluster. Here, we generalize this model to multiple species and present a general framework to infer ancestral gene orders that minimize the number of inversions in the whole evolutionary history. An application on a pair of human-rat TAG clusters is presented.