Observations of extremely high brightness temperatures in astrophysical objects imply that coherent emission processes must be occurring. An emission process may be coherent due to an inverted energy distribution leading to maser action, or due to bunching of particles in a region less than or of order of the wavelength of the radiation. Calculations of emission by bunches have generally used either a fluid model, e.g. Buschauer and Benford (1976), or a single-particle approach which requires all particles to have the same velocity, e.g. Saggion (1975) uses elements of both. In this paper we investigate gyromagnetic emission by bunches using a single-particle approach which includes the effects of differing particle velocities on the radiation.