1. In a series of behavioural experiments designed to measure spatial acuity, freely-flying honeybees were trained to discriminate between a horizontal and a vertical grating in a Y-shaped, dual-tunnel apparatus (Fig. 1). Each grating was placed at the entrance to a tunnel, and one of the gratings carried a reward of sugar solution. After training, the spatial frequency of the two gratings, as seen from the tunnel entrances, was varied by varying, symmetrically, their distances from the tunnel entrances. At each spatial frequency, the bees' response (percentage correct discriminations) was calculated from the number of entrances that they made into the tunnels associated with the rewarded and unrewarded gratings, to obtain Response-versus-spatial-frequency (RSF) curves (Figs. 3–5, 10–12). 2. In general, response decreases with increasing spatial frequency. With black-and-white gratings, the RSF curve exhibits a corner spatial frequency (corresponding to a response level of 65%) of ca. 0.25 cycles per degree of visual angle (c/deg), and the response is statistically indistinguishable from the 50% level (corresponding to random choice) at a spatial frequency of ca. 0.34 c/deg (Figs. 3, 4). 3. The shape of the RSF curve does not depend upon which grating is rewarded (horizontal or vertical). Similar RSF curves are also obtained when bees are trained to discriminate a horizontal or a vertical grating from a uniform grey field (Figs. 4, 5). These results imply that the acuities in the horizontal and vertical plane at the front of the eye are essentially equal for freely-flying bees. 4. An independent estimate of spatial acuity was derived by analysing video-films of the bees' flight trajectories when they approached the incorrect stimulus (Figs. 6–9). This analysis estimates acuity to be slightly poorer (corner spatial frequency: ca. 0.18 c/deg) than that inferred from the RSF curves. The films also confirm that the bees use the frontal regions of their eyes in making the visual discrimination (Fig. 10). 5. Detailed observation of the bees' decision behaviour indicates that, when the stimuli in the two tunnels cannot be distinguished at the tunnel entrances, each individual choice that a bee makes between the two tunnels tends to be independent of the outcome of the previous choice. That is, the success or failure of a choice is not memorized. 6. Comparison of acuity measured behaviourally with that predicted from the optical characteristics of the compound eye, reveals that the bees' capacity to discriminate orientation of linear gratings is limited primarily by the size of the visual fields of individual photoreceptors. 7. Experiments conducted using grey gratings, and dual-colour gratings which provide contrast exclusively to a single spectral class of receptors (blue or green) reveal that orientation discrimination of vertical and horizontal high-spatial-frequency gratings is mediated chiefly by the greenreceptor channel, and is therefore colour-blind (Figs. 10–13). 8. Experiments investigating orientation discrimination of dual-colourradial gratings reveal an acuity that is poorer andnot colour-blind (Fig. 14). We suggest that, besides the high-acuity colour-blind mechanism, there is another mechanism that is not colour blind, works on the basis of a memorized, colour-coded spatial template, and has lower spatial acuity.