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The GDH sum rule is discussed for the Delta(1232) resonance. It is shown thatapart from ordinary excitations to higher-energy states, the sum rule containsa large negative contribution due to de-excitation into the nucleon state.Therefore, a fulfillment of the sum rule assumes a strong coupling of Delta^+and Delta^0 to resonances of spin 5/2 and higher. Calculations performed inquark models suggest that D15(1675) may be such a resonance. However, itsstrength is found to be not sufficient for bringing the GDH sum rule to atheoretically expected positive magnitude.Comment: 5 pages, no figures. Extended talk at the GDH2000 Symposium, Mainz,  June 14-17, 2000. To appear in proceeding

THE GDH SUM RULE FOR THE Δ ISOBAR: A POSSIBLE ANOMALY?