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(∆ 3 f ), where ∆ f is an N f -dependent expansion variable. Our general results are evaluated for several special cases, including the case G = SU(Nc) with R equal to the fundamental and adjoint representations.τ Oi,n = d Oi,n − j Oi,n ,(1.5) with j Oi,n = n here. Thus, among bilinear fermion operators, in addition toψγ µ1 ψ with dimension 3, spin 1, and hence τ = 2, there are the operatorsψγ µ1 D µ2 · · · D µj ψ, with dimension 3 + (j − 1) and spin j, which also have τ = 2. These are the minimum-twist bilinear fermion operators that contribute to the light-cone OPE (1.3)