Properties of resonance cones in non-Maxwellian plasmas are examined and compared with those in Maxwellian plasmas. The dispersion relations and the potential of a point charge in a current-carrying non-Maxwellian plasma with a beamlike or a long flat tail of the electron distribution functions are investigated with the approximation of a large magnetostatic field. In the case of a beam, when the beam velocity is well above the thermal velocities of the beam and bulk electrons, the Cerenkov instability occurs. In this case the wave number spectrum k∥ > ω/νb becomes unstable, where νb is the beam velocity, ω is the frequency, and k∥ is the wave number parallel to the magnetic field. The Cerenkov instability causes strong radiation near a conical surface called the Cerenkov cone. When νb is not very large, the Cerenkov cone angle is found to be considerably smaller than the resonance cone angle, thus there are two distinct angles corresponding to the Cerenkov and resonance cones, where the radiation peaks. The Cerenkov cone peak grows with increasing distance from the source, while the resonance cone peak decays. For the situations when the resonance cone peak is not affected by the Cerenkov instability, we have compared the angular shifts of the resonance cone peaks caused by the same current in Maxwellian and non-Maxwellian plasmas. This comparison throws light on the resonance cone technique for measuring magnetic field-aligned currents in plasmas. It is found that a long flat tail to the bulk electron distribution function gives a characteristic split to the resonance cone peak in the downstream of the electron flow, an observation of this split can be used as an indication of the existence of the long tail.