The classification of hybrid modes in cylindrical dielectric waveguides consisting of two or three layers is studied. A new mode designation based upon the separation of the characteristic equation is introduced. That is, separate characteristic equations for HEnm and EHnm modes are derived. This new scheme covers dielectric rods, dielectric tubes, cladded optical fibers and any three-layer structure in general. It is analytically shown that no crossover exists between HE and EH modes with the same order of azimuthal variation (n).