It has been shown by a number of investigators that perceived binocular direction (BD) could be changed by varying the contrast ratio between the left and right images of a target. In this and certain other cases, the former simple idea that BD is the average of the two monocular directions (MD) fails to predict BD correctly. As an alternative, Mansfield and Legge (1996 Vision Research 36 27 – 41) suggested that a weighted average of modified MD signals be calculated with weights depending on respective image contrasts. However, in experiments including not only ordinary (monocularly recognisable) but also cyclopean (monocularly imperceptible) targets, we have found that there exist (at least) two principally different mechanisms responsible for calculation of BD and that one of these mechanisms is contrast-dependent while the other one is contrast-independent (Rozhkova et al, 1995 Sensory Systems 9 46 – 57). The first one probably corresponds to the model of Mansfield and Legge but the second one (which determines perception of cyclopean targets) has other specific properties. In a new series of experiments based on the same paradigm (to align a test target with a control one under conditions of varying interocular contrast ratios for the test stimuli), we have found that perceived direction of a cyclopean target (coded by Julesz's random-dot stereogram) could be manipulated by memory. It appeared that if, in a given series of measurements, the random-dot patterns for the test targets were chosen at random from six samples, the results were independent of the contrast ratio, but if one and the same random-dot pattern was used many times throughout all the series of measurements, and the subject could memorise the texture of the target, perceived direction became dependent on contrast ratio as in the case of monocularly recognisable targets. One of the possible explanations of this effect is the secondary activation of the first BD mechanism, which usually does not process cyclopean targets.