Unsteady propagation and instability of radiative stretched premixed flames at Lewis numbers close to unity were numerically investigated using helium-diluted counterflow methane flames, with the interest on understanding the stability of three near-limit and sublimit multiple flame regimes, namely, the near stagnation flame, the weak flame, and the distant flame. It is shown that both the near-limit and sublimit near-stagnation flames are stable close to the flammability limit and that a new mode of oscillation instability exists at equivalence ratios sufficiently larger than the flammability limit. In addition, stability of the weak and the distant flames is demonstrated, while unsteady mutual transitions between the near-stagnation flame and the distant flame and jump from the weak flame to the normal flame are found. A comparison of the present prediction with the microgravity experimental observation shows qualitative agreement on the oscillation frequency and region for the occurrence of oscillation. Calculations for Lewis numbers larger and smaller than unity show that the radiation-induced instability is a physically intrinsic phenomenon for radiative stretched premixed flame. The present study provides a satisfactory explanation for the microgravity observation.