The use of discrimination learning paradigms in the study of attentional transfer is discussed. The technique of go/no-go discrimination learning followed by stimulus generalization testing is contrasted with the more familiar simultaneous learning paradigm followed by a shift in the relevant cues. In the former paradigm the effect of training a discrimination on one dimension on the slope of the stimulus generalization gradient on an independent gradient dimension (extra-dimensional training) is assessed. A steepening of the gradient relative to appropriate control procedures is taken as evidence of positive attentional transfer. The relevance of the technique to the detailed study of attentional transfer in educationally subnormal (severely) (ESN(S)) children is considered. In Expt. I nine ESN(S) children were trained in a go/no-go discrimination involving stimuli differing in orientation, and were generalization tested on a dimension that was orthogonal, namely hue. Of the six subjects who learnt the discrimination five showed clear decremental gradients on the hue dimension. In contrast a Pseudo-Discrimination group (PD) of eight subjects matched to those in the TD group showed no gradients. These subjects were not trained in the orientation discrimination, but were reinforced for responding on 50 per cent of each of the S+ and S- stimulus presentations. They thus received equal exposure to, but no differential training on, the orientation dimension. An S+ only group of four subjects who received no exposure to the orientation stimuli showed no gradients when stimulus generalization testing on the hue continuum was carried out. The result is discussed in terms of transfer deriving from stimulus control by relational aspects of the stimuli; in terms of control by constant irrelevant stimuli; and in terms of the study of stimulus control in ESN(S) children. In Expt. II the influence of the codability of the colours on the location of the peak of the stimulus generalization gradients in the TD group is investigated.