ABSTRACT. Magnetic flux quanta, of value h/2e, in long Josephson junctions behave as (quasi) solitons. Fluxon dynamical states are well described by a perturbed sine-Gordon equation model, with boundary conditions determined by the junction geometry and by externally applied magnetic fields, and they give rise to readily measurable physical phenomena, such as step structure in current-voltage characteristics and microwave radiation emission. Devices based on fluxon propagation offer potentially interesting applications as oscillators and amplifiers-as well as digital applications, described elsewhere in this volume-in high performance integrated superconductive circuits.