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In models with dynamical supersymmetry breaking in the hidden sector, the gaugino masses in the observable sector have been believed to be extremely suppressed (below 1 keV), unless there is a gauge singlet in the hidden sector with specific couplings to the observable sector gauge multiplets. We point out that there is a pure supergravity contribution to gaugino masses at the quantum level arising from the superconformal anomaly. Our results are valid to all orders in perturbation theory and are related to the 'exact' beta functions for soft terms. There is also an anomaly contribution to the A terms proportional to the beta function of the corresponding Yukawa coupling. The gaugino masses are proportional to the corresponding gauge beta functions, and so do not satisfy the usual GUT relations.