High‐frequency electromagnetic waves guided by an air‐bounded, axially magnetized, plasma column of radiusaare studied through the technique of parameter space mapping. The parameter space is 3‐dimensional with coordinates &ohgr;p/&ohgr;, &ohgr;b/&ohgr;, andc/&ohgr;a. In this 3‐space, cutoff and resonance loci form surfaces which enclose approximate domains of existence for various classes of waves.Three wave classes, characterized by distinctive cutoff and resonance surfaces, are identified for a magnetized plasma column, and their relation to waves in a boundless plasma, and on a column of small radius (quasistatic waves) is investigated. Also, evidence is found for the continued existence of the surface wave class into the regime &ohgr;b>&ohgr;p.Parameter space analysis leads to a determination of salient dispersion characteristics for all wave classes and all order of azimuthal variation by a method contributing to physical insight but which avoids exact but laborious numerical computation. Waves are found which change from forward to backward or vice versa with increasing wave number.