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In this paper we consider a process of plane wave scattering from a single dielectric cylinder at oblique incidence under which it is possible to excite long range cyclic Sommerfeld waves (CSWs) and consequently cyclic Sommerfeld resonances (CSRs) of different orders. It is shown that the CSRs are analogous to Wood's anomalies occurred under plane wave scattering from one dimensional (1D) metallic diffraction gratings. The conditions which are necessary for an effective excitation of CSWs and CSRs with high quality factors are analyzed.