An excitable system admits a stable state but may be destabilized by small perturbations. In an extended uniform media the perturbation will take the form of a travelling pulse. The motion is different in a fixed bed due to its finite length and the direction imposed by the flow. Such a motion has been recently observed in an adiabatic Pt/Al2O3 bed catalyzing ethylene oxidation: fronts produced by an extinction at the inlet always travel downstream and exit and the reactor while a hot spot develops at the inlet and spreads downstream by increasing the temperature to the ignition point. A simple mathematical model of an excitable fixed bed is constructed and its rich dynamics is analyzed in order to develop a methodology for motion identification and classification. Transients are composed of four basic elementary motions: these are classified according to the expanding domain, ignition or extinction, and the front direction, upstream or downstream. Imposing ignition at the outlet, for example, yields a constant-velocity front that travels upstream. The subsequent extinction may occur at the inlet, outlet or in between. Imposing an extinction at the inlet produces the scenario observed experimentally. Under certain conditions a train of fronts, moving up- or downstream, may be realized.