  We reconsider the cosmic string perturbative solution to the classical
fourth-order gravity field equations, obtained in Ref.\cite{CLA94}, and we
obtain that static, cylindricaly symmetric gauge cosmic strings, with constant
energy density, can contain only $\beta$-terms in the first order corrections
to the interior gravitational field, while the exact exterior solution is a
conical spacetime with deficit angle $D=8\pi\mu$.
