The solutions of nonaxisymmetric fields in SELFOC fibers with longitudinal imperfections are investigated. The refractive index is assumed to be of the form

(

is a gradually varying function of

). The analytic solution is obtained. When K
2is a constant, the solution is reduced to that of perfect SEL-FOC fibers, which is well known. Further the relations of modes conversion in imperfect fibers are obtained.