The characteristics of the flame structure, stabilization, and extinction of counterflow nonpremixed flames of CH4/He versus air at low strain rates are investigated by performing a series of experiments and two-dimensional (2-D) numerical simulations. By adopting an experimental methodology using He curtain flow, we can locate the flames near the center of the counterflow burner and measure the critical He mole fraction in the fuel stream, XHe,cr, for flame extinction at very-low strain rates. XHe,cr obtained from 2-D numerical simulations in normal and zero gravity show a good agreement with those from the experiments, which substantiates that the experimental methodology can effectively reduce the buoyancy effect at low strain rates. It is found from various steady and unsteady 2-D numerical simulations that the dynamics of flame edge plays a critical role in determining the flame stabilization and extinction, and the edge flame is stabilized at a location where negative edge flame propagation speed, Se, balances positive local flow velocity, Ue. The transport budget analysis reveals that despite the negative Se by the diffusive loss of heat and radicals, the edge flame can survive by the help of the convective gain of heat and radicals from the trailing diffusion flame. It is also found that the counterflow flame can survive the increase of He mole fraction in the fuel stream, XHe, by shrinking its flame length since the local chemical reaction at the flame edge is enhanced with decreasing the flame length. However, as XHe exceeds XHe,cr, a slight inward movement of the edge flame induces a large magnitude of negative Se compared to positive Ue such that the counterflow flame is totally extinguished by the shrinkage of the outer edge flame toward the flame center.