We consider an asymptotically free vectorial gauge theory, with gauge group $G$ and $N_f$ fermions in a representation $R$ of $G$, having an infrared fixed point of the renormalization group. We calculate scheme-independent series expansions for the anomalous dimensions of higher-spin bilinear fermion operators at this infrared fixed point up to $O(Delta_f^3)$, where $Delta_f$ is an $N_f$-dependent expansion variable. Our general results are evaluated for several special cases, including the case $G={rm SU}(N_c)$ with $R$ equal to the fundamental and adjoint representations.
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