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A cancellation of conformal anomalies in d=4 for the $C^2+\bar C^2$ and ofchiral anomalies for the $C^2-\bar C^2$ is known in N-extended supergravitieswith $N \geq 5$. We propose an explanation of these cancellations usingsupersymmetry and dimension of linearized chiral superfields. We contrast thesemodels with the ones with $N < 5$, where both types of anomalies are known tobe present.

Cancellation of Conformal and Chiral Anomalies in $N \geq 5$ supergravities