The Tj¿rnes Fracture Zone is a transform fault connecting the rift zone of the Kolbeinsey Ridge with that of north Iceland. The main transform motion takes place on the H¿sav¿k-Flatey Fault, a major 7--9 Myr old right-lateral fault. In addition to this fault, there are two major seismic lineaments associated with the Tj¿rnes Fracture Zone; the Gr¿msey lineament and the Dalv¿k lineament. These lineaments are marked by concentrations of seismicity with the largest earthquakes reaching magnitude 7. The maximum depth of earthquakes is 10--12 km and increases with distance from the spreading axis. We determined accurate relative locations and focal mechanisms of more than 800 earthquakes in 62 clusters on the principal seismic lineaments. The estimated relative location uncertainty for most of the relocated earthquakes is 2--20 m. The best fitting plane through each cluster is assumed to coincide with the fault plane of the group of earthquakes. For clusters near the H¿sav¿k-Flatey Fault the fault planes are right-lateral and strike N122 ¿E--N140 ¿E, similar to the overall strike of the H¿sav¿k-Flatey Fault. This agrees with the right-lateral displacement on the fault as well as with field observations of numerous transform-parallel right-lateral faults associated with the main fault. By contrast, earthquake clusters on the lineaments of Gr¿msey and Dalv¿k define (mostly) left-lateral planes striking roughly north-south, i.e., at 40¿--90¿ to the overall trend of these lineaments. Field observations show that left-lateral, north-south trending fault planes are also common in the on-land parts of the Dalv¿k lineament. The different style of faulting probably represents transform faults at different stages of development. ¿ 1998 American Geophysical Union