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The heavy quark effects in deep--inelastic scattering in the asymptoticregime $Q^2 \gg m^2$ can be described by heavy flavor operator matrix elements.Complete analytic expressions for these objects are currently known to ${\sfNLO}$. We present first results for fixed moments at ${\sf NNLO}$. Thisinvolves a recalculation of fixed moments of the corresponding ${\sf NNLO}$anomalous dimensions, which we thereby confirm.

Heavy flavor operator matrix elements at $O(a_s^3)$