Spatiotemporal patterns existing in a one‐dimensional fixed‐bed reactor with oscillatory or excitable kinetics are analyzed to develop the methodology of motion identification and classification. The reactor model accounts for a local (solid‐phase) oscillator and a global (gas‐phase) convective interaction. The local oscillator incorporates a fast and diffusing surface temperature and a localized activity as its dynamic variables. Such kinetics admit a traveling pulse solution or homogeneous oscillations in a uniform medium. In a fixed‐bed reactor, the local conditions in the bed (the phase plane character) vary along the system. The response of an excitable bed to local perturbations depends on its location (at inlet or outlet) and the nature of the initial steady state ( ignite or extinguished). The main spatiotemporal‐sustained patterns in the bed are: almost homogeneous oscillations that appear as parallel bands in the time‐space contour map; oscillatory fronts that emerge from the reactor exit, and aperiodic motion that appears as split‐bands. Pattern selection is determined by the phase planes spanned by the reactor and the ratio of the two slowest time scales: front residence time and period of oscillations.