Linear coupling effects due to skew quadrupole fields have become more important for proton synchrotrons. Large tune shifts can be generated by linear coupling. A higher order tune shift, roughly quadratic in the skew quadrupole field, may be present, which may require a more complex correction system. There may be large shifts in the beta functions, and some reduction in the dynamic aperture. Analytical results have been found for the higher order tune shift and the beta function shifts. Numerical results for these effects are given for RHIC, and a correction system is proposed for these effects. A correction system with about 4 or 5 families of skew quadrupole correctors appears able to correct the above effects.