Recent studies have revealed that navigating honeybees, Apis mellifera, estimate the distance to a food source by integrating over time the image motion that they experience en route. Here we examine the ability of honeybees to gauge distance travelled when visual input is available primarily to one eye. Bees were trained to fly into a tunnel, lined with textured patterns, to collect a reward at a feeder placed at a certain distance. Their ability to estimate distance flown was then assessed by testing them in a fresh tunnel without the feeder. The results show that (1) bees can estimate distance flown under monocular conditions, performing nearly as accurately as when information is available to both eyes; (2) bees can learn to fly two different distances, where each distance is measured in terms of the image motion experienced by a different eye; and (3) bees that have acquired information on the distance to a food source using one eye can measure out the same distance when they are required to use the other (naive) eye. The need to measure distance using signals from a single eye becomes important when a bee flies to a food source along the face of a cliff or the edge of a forest. Furthermore, under such conditions, it is important to be able to deal with odometric signals that are transposed interocularly when the bee returns home from the food source. This is because, although distances are learnt primarily on the way to a food source, foraging bees monitor distance flown on the homebound as well as the outbound routes. Copyright 1998 The Association for the Study of Animal Behaviour.