The field produced by a quadrupole magnet is antisymmetric with respect to reflection through either of two orthogonal planes whose intersection is the optical axis of the magnet. Failure to perfectly align these planes for a given quadrupole magnet with the cardinal planes of the beam system incorporating that magnet induces an error field that perturbs the beam. The effects of misalignments of a number of quadrupoles are derived by including the induced error fields in the equation of motion. The results are expressed in terms of the known linear optical properties of the beam system and are sufficient for determining the tolerances required on each constituent quadpole magnet.