Thirty gifted children were allocated at random to either progressive muscle relaxation or EMG biofeedback treatment groups or to a no‐treatment, control group. At the outcome, the biofeedback group evinced a significant decrease in state anxiety and both groups moved towards a more internal locus of control compared with the untreated group. There was no change, however, in trait anxiety. The supposition that gifted children are more anxious than non‐gifted children was not borne out. The implications of these findings are discussed.