The key issue of the study is extension of the technique set forth in [1–3] to clarify and justify the nature of resonance phenomena observed for cylindrical open structures at real frequencies. When the plane electromagnetic wave diffraction by an open layered-dielectric scatterer possessing radial symmetry is considered and the corresponding boundary-value problem is solvable in cylindrical coordinates using separation of variables, the solution is represented as series in outgoing harmonics where the expansion coefficients are determined explicitly [1, 2] and in the form which enables one to calculate simultaneously the parameter sets when (i) a certain quantity of the principal expansion terms vanish and (ii) individual expansion coefficients have singularities (the latter yields resonances of the considered open structure). This fact paves the way to apply the analysis of multi-parameter Fourier series to the study of the scattered-field expansion coefficients and to determine the parameter values at which not only the partial invisibility and cloaking take place (caused by the suppression of the scattered-field harmonics), but also other well-known resonance phenomena.