The effects of thermal radiation and stretch on the dynamics of premixed and diffusive flames of near limit dimethyl ether mixtures are numerically simulated using in a counterflow geometry at elevated pressures. The primary focus is to understand how thermal radiation affects the flame regimes and extinction limits of cool flames and hot flames in a stretched flow. The results show that radiation has a dramatic effect on the dynamics of near limit flames with cool flame chemistry. For adiabatic premixed flames, the results show that both hot and cool flames exist at near limit flame conditions. At higher equivalence ratio, hot flames have higher stretch extinction limits than cool flames. However, as the equivalence ratio decreases, cool flames have higher stretch extinction limits than hot flames. With the combined effect of thermal radiation and stretch, the results show that even for the mixture Lewis number greater than unity, a sub-limit hot flame can exist in a finite range of stretch rates bounded, respectively, by the radiation extinction limit at a low stretch rate and the stretch extinction limit at a high stretch rate. Moreover, it is found that thermal radiation has much smaller effect on cool flames than hot flames. It is found that cool flames can exist at an equivalence ratio far below the flammability limit of the hot flames. For diffusion flames, the results show that the fuel and oxygen concentrations affect significantly the flame regimes and the extinction limits of hot and cool flames. At lower fuel and oxygen concentrations, there exist three different flame regimes, hot flame, intermediate temperature flame, and cool flame. Moreover, as the oxidation concentration further decreases, it is shown that radiation extinction occurs at a low stretch rate, resulting a radiation extinction transition from hot flame to cool flame.