Limits of flammability are discontinuities in the flame propagation rate at finite fuel concentrations. Their existence is caused by competing loss processes that dissipate power from an ideal combustion wave. This study considers the loss process associated with flame propagation into flow gradients; namely, flame stretch. For divergent, spherical propagation from an ignition kernel of radius r, the limit burning velocity for flame stretch is (Su)e=(2 ∞/r) (ρu/ρb). For propagation into a preexisting, stretching velocity gradient of magnitude dv/dx, the limit burning velocity is (Su)e=[∞ dv/dx]1/2. Those limit burning velocity concepts are shown to be fully equivalent to the following: extinction at a critical, flame-zone Damkohler number of Da≤1; extinction at a critical Karlovitz number of K≥1; the Markstein equation for the effect of flame curvature on the local burning velocity. Literature data for the blow-off limits of flames are shown to give excellent agreement with those extinction criteria, provided that proper account is taken of the effects of dilution: composition dilution caused by entrainment and velocity gradient dilution caused by flow expansion. Extrapolation to zero plate thickness of the best available inverted flame data is required in order to overcome those problems. The resultant (dv/dx) (limit)-values obtained are in excellent agreement with the theory. For the normal or earthy limits of flammability, it is natural convection that generates the velocity gradients responsible for stretch extinction. Approximate, flow-field solutions are derived for the unburned gas motions above an upward propagating, spherical-flame kernel in its unconfined state, in the presence of the buoyancy-induced flows generated by the flame's own irreversible, exothermic reactions. The upward hemisphere propagates toward a stagnation plane in a counterflow configuration which is generated by the balance between the combustion-force expansion, which accelerates the cold gas upward, and the buoyancy force couple, which accelerates the cold gas downward. The position of the stagnation plane is controlled by the ratio of the buoyant velocity, vh, to the burning velocity, Su. Extinction occurs by flame stretch in that counterflow configuration when η=vb/Su begins to exceed the expansion ratio, ρu/ρb, and the wave is blown off by its own, buoyancy-induced flows.