An analysis is presented of the radiation emitted by an arbitrary source embedded in a cold, magnetoactive plasma and physically distinct from the latter. The plasma is supposed to be infinite and homogeneous; its dielectric properties are described by a dielectric tensor &egr;. Expressions for the radiation fields are derived using the technique of Fourier decomposition. An expression for the vector potential is constructed and elaborated as far as possible for anarbitrarycurrent source. The approach differs from that in previous work on technical points, the main one being the sequence in which the various integrations are carried out. The radiation flux is defined on the basis of Poynting’s vector S; a distinction is made between current sources behaving as a given function of time and randomly fluctuating sources. In the latter case an ensemble average is preferred over a time average. A comparison is made with existing treatments in the literature, and a variety of defects is pointed out. The general result for the radiation flux is then specified for cyclotron radiation from a stationary ensemble of electrons and for multipole radiation. Throughout the paper a compact notation is used based on the work of Bremmer.