We propose that the Caribbean (Ca)--North American (NA) plate boundary zone (pbz) from the Puerto Rico Trench to the Venzuelan Basin from Mona Canyon east has been in left-transtension over the last 15--20 ma. A boundary-normal component of extension occurs throughout the pbz and is a principal cause of the Puerto Rico Trench. Such extension is due to WNW velocity of Na-Ca and the northward pullaway of Na from its S-dipping slab, which is below Puerto Rico. Strike slip motion may be taken up among terranes in the pbz by rigid CCW rotation and by oblique slip at their boundaries. Rotation of the largest terrane, Puerto Rico--Virgin Islands (PRVI), has caused such major structures as the Muertos thrust and Anegada Passage. The model implies NA-Ca velocity estimated from Cayman transforms is more accurate than that from slip vectors from seisms in the NA slab. ¿American Geophysical Union 1991