This paper discusses the syntactic representation of participial dependents of modal verbs in Basque, their internal structure and their position with regard to the matrix modal verb. The analysis focuses on those varieties that admit the participial dependent to occur either before or after the modal verb. It is shown that in those varieties, the syntactic position of the participial dependent correlates with differences in its internal structure: whereas participial dependents can correspond to TPs when they are located to the right of the modal verb in Basque (a typically SOV language), they cannot correspond to anything more complex than a small v structure to the left of the modal verb. Our analysis of the internal structure of participial dependents also extends to issues concerning the basic word order of Basque. It is claimed that the analysis presented here requires the auxiliary to be generated to the left of the verb phrase, as the antisymmetry hypothesis would have it.