Resonant fluxon propagation on an overlap‐geometry Josephson tunnel junction of length 5&lgr;Jhaving a McCumber &bgr;c=5&pgr; is studied by numerical integration of the circuit equations of a 50‐section lumped RSJ‐type model. The zero‐field steps in the dc current‐voltage characteristic of the junction deriving from the two lowest order resonant fluxon configurations are calculated, and the switching mechanisms defining the upper and lower current thresholds are described. The power spectra of the radiation emitted from one end of the junction when it is current biased on each of these two zero‐field steps is calculated assuming negligible loading. An applied dc magnetic field is shown to cause a small increase in the frequency of this radiation, in contrast with reported experimental measurements.