The automatic alignment system for the two suspended, triangular mode-cleaner cavities of the gravitational wave detector GEO 600 has been in continuous operation since the spring of 2001. A total of 20 angular degrees of freedom are controlled by feedback loops with almost no manual alignment having been required since installation. Error signals for the eight most important degrees of freedom are obtained with the differential wave-front sensing technique. We describe the sensing system, the control topology, and the performance of the automatic alignment system. A continuous locking stretch of more than 120 h has been achieved.