This paper examines the hybrid-cladding modes of an eccentrically cladded three-layer dielectric fiber. The solutions are specialized to small eccentricities, and exact closed-form expressions for the normalized deviations of the cutoff wavenumbers from those of the concentric case are determined. Numerical results for various types of hybrid-cladding modes of the fiber are given. For certain values of the parameters, it is possible to enhance the operating bandwidth of the basic hybrid mode HE/sub 11/ over the conventional concentric fiber because its cutoff frequency can be shown to remain zero.