When the head rotates, the image of the visual world slips across the retina. A dedicated set of retinal ganglion cells (RGCs) and brainstem visual nuclei termed the "accessory optic system" (AOS) generate slip-compensating eye movements that stabilize visual images on the retina and improve visual performance. Which types of RGCs project to each of the various AOS nuclei remain unresolved. Here we report a new transgenic mouse line, Hoxd10-GFP, in which the RGCs projecting to all the AOS nuclei are fluorescently labeled. Electrophysiological recordings of Hoxd10-GFP RGCs revealed that they include all three subtypes of On direction-selective RGCs (On-DSGCs), responding to upward, downward, or forward motion. Hoxd10-GFP RGCs also include one subtype of On-Off DSGCs tuned for forward motion. Retrograde circuit mapping with modified rabies viruses revealed that the On-DSGCs project to the brainstem centers involved in both horizontal and vertical retinal slip compensation. In contrast, the On-Off DSGCs labeled in Hoxd10-GFP mice projected to AOS nuclei controlling horizontal but not vertical image stabilization. Moreover, the forward tuned On-Off DSGCs appear physiologically and molecularly distinct from all previously genetically identified On-Off DSGCs. These data begin to clarify the cell types and circuits underlying image stabilization during self-motion, and they support an unexpected diversity of DSGC subtypes.