Combustion experiments on polypropylene (PP) and polyethylene terephethalate (PET) in stagnation-point flow were performed to investigate the fundamental characteristics of these polymers in high-temperature air combustion (HiTAC). Numerical study was also performed to estimate the regression rate and to determine the kinetic parameter of pyrolysis. In the experiments on PP combustion, extinction limits and sooting limits were found to be extended when highly preheated air was used. In the case of H2O and CO2 dilutions, the dilution enhanced regression rates at low stretch rates. In the case of PET combustion, results indicated that regression rates depended on the production rate of char. The kinetic parameters of PP pyrolysis under the combustion conditions were estimated using a new method in which experiments and numerical simulations were combined. The regression rates calculated using the kinetic parameters obtained in the present study were in good agreement with those of the experiments in contrast with the numerical results using the kinetic parameters obtained using the previously reported thermal gravimetric analysis (TGA).