Abstract This article concerns a theoretical study of combustion in a stretched, one-dimensional carbon monoxide (CO) strip surrounded by air. The analysis includes the effects of radiative heat transfer and time-dependent strain. Solution of mass, species, and energy equations for a single-step, finite-rate reaction between CO and O 2 is obtained for an externally imposed in-plane strain motion with strain rates up to 1000 s −1 and for several strain rate histories. The radiation heat loss from the flame zone to its surroundings is incorporated into the solution using the optically thin gas radiation approximation. The results indicate that unstretched flames are significantly influenced by the presence of radiative heat loss, resulting in thermal quenching. Although, CO consumption rates in positively stretched flames are unaffected by the effects of radiative heat loss, the structure of the flame zone is somewhat altered. The CO oxidation behavior is found to be dependent on the strain history. Although low-frequency (of the order of inverse diffusion time scale) fluctuations in the strain rate enhance the CO oxidation significantly, the flame does not respond to fast oscillations. Radiative heat losses can promote quenching during negative (compressive) strain periods in the strain history.