The nonlinearly induced nonreciprocity of counterpropagating waves caused by an index grating in a Kerr medium can be used to nonlinearly enhance the Sagnac effect in a ring resonator. A specific discussion of this effect in the case of a fiber-optic rotation sensor is presented. Our theory, which holds for any value of the cavity finesse, includes transverse effects explicitly, but neglects stimulated scattering. Special emphasis is given to pure cavity effects which always occur simultaneously with the nonlinear Sagnac effect. © 1985 The American Physical Society.