Abstract
We present the correct expression for conformal anomaly in Weyl theory implying its perturbative non-renormalizability. As a by-product it is found that non-singular cosmologies exist in quantized Weyl theory. The absence of conformal anomalies in theories incorporating local conformal invariance is proposed as necessary requirement for their consistency. Several superconformal theories, including N=4 SU 2×U 1 super Yang-Mills interacting with N=4 conformal supergravity, are shown to satisfy this restriction, i.e. to be completely finite (at least at one loop).
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