Extensive chemical characterization of ozone (O3) depletion events in the Arctic boundary layer during the TOPSE aircraft mission in March--May 2000 enables analysis of the coupled chemical evolution of bromine (BrOx), chlorine (ClOx), hydrogen oxide (HOx) and nitrogen oxide (NOx) radicals during these events. We project the TOPSE observations onto an O3 chemical coordinate to construct a chronology of radical chemistry during O3 depletion events, and we compare this chronology to results from a photochemical model simulation. Comparison of observed trends in ethyne (oxidized by Br) and ethane (oxidized by Cl) indicates that ClOx chemistry is only active during the early stage of O3 depletion (O3 > 10 ppbv). We attribute this result to the suppression of BrCl regeneration as O3 decreases. Formaldehyde and peroxy radical concentrations decline by factors of 4 and 2 respectively during O3 depletion and we explain both trends on the basis of the reaction of CH2O with Br. Observed NOx concentrations decline abruptly in the early stages of O3 depletion and recover as O3 drops below 10 ppbv. We attribute the initial decline to BrNO3 hydrolysis in aerosol, and the subsequent recovery to suppression of BrNO3 formation as O3 drops. Under halogen-free conditions we find that HNO4 heterogeneous chemistry could provide a major NOx sink not included in standard models. Halogen radical chemistry in the model can produce under realistic conditions an oscillatory system with a period of 3 days, which we believe is the fastest oscillation ever reported for a chemical system in the atmosphere.