Eye or head rotation would influence perceived heading direction if it were coded by cells tuned only to retinal flow patterns that correspond to linear self-movement. We propose a model for heading detection based on motion templates that are also Gaussian-tuned to the amount of rotational flow. Such retinal flow templates allow explicit use of extra-retinal signals to create templates tuned to head-centric flow as seen by the stationary eye. Our model predicts an intermediate layer of 'eye velocity gain fields' in which 'rate-coded' eye velocity is multiplied with responses of templates sensitive to specific retinal flow patterns. By combination of the activities of one retinal flow template and many units with an eye velocity gain field, a new type of unit appears: its preferred retinal flow changes dynamically in accordance with the eye rotation velocity. This unit's activity becomes thereby approximately invariant to the amount of eye rotation. The units with eye velocity gain fields from the motion-analogue of the units with eye position gain fields found in area 7a, which according to our general approach, are needed to transform position from retino-centric to head-centric coordinates. The rotation-tuned templates can also provide rate-coded visual estimates of eye rotation to allow a pure visual compensation for rotational flow. Our model is consistent with psychophysical data that indicate a role for extra-retinal as well as visual rotation signals in the correct perception of heading.