Foam can improve sweep efficiency in gas-injection-enhanced oil recovery. Surfactant-alternating-gas (SAG) is a favored method of foam injection. Laboratory data indicate that foam can be non-Newtonian at low water fractional flow f_w, and therefore during gas injection in a SAG process. We investigate the implications of this finding for mobility control and injectivity, by extending fractional-flow theory to gas injection in a non-Newtonian SAG process in radial flow. We make most of the standard assumptions of fractional-flow theory (incompressible phases, one-dimensional displacement through a homogeneous reservoir, instantaneous attainment of local equilibrium), excluding Newtonian mobilities. For this initial study, we ignore the effect of changing or non-uniform oil saturation on foam. Non-Newtonian behavior at low f_w implies that the limiting water saturation for foam stability varies as superficial velocity decreases with radial distance from the well. We discretize the domain radially and perform Buckley–Leverett analysis on each narrow increment in radius. Solution characteristics move outward with fixed f_w. We base the foam model parameters and non-Newtonian behavior on laboratory data in the absence of oil. We compare results to mobility and injectivity determined by conventional simulation, where grid resolution is usually limited. For shear-thinning foam, mobility control improves as the foam front propagates from the well, but injectivity declines somewhat with time. This change in mobility ratio is not that at steady state at fixed water fractional flow in the laboratory, however, because the shock front in a non-Newtonian SAG process does not propagate at fixed fractional flow (though individual characteristics do). Moreover, the shock front is not governed by the conventional condition of tangency to the fractional-flow curve, though it continually approaches this condition. Injectivity benefits from the increased mobility of shear-thinning foam near the well. The foam front, which maintains a constant dimensionless velocity for Newtonian foam, decelerates somewhat with time for shear-thinning foam. For shear-thickening foam, mobility control deteriorates as the foam front advances, though injectivity improves somewhat with time. Overall, however, injectivity suffers from reduced foam mobility at high superficial velocity near the well. The foam front accelerates somewhat with time. Conventional simulators cannot adequately represent these effects, or estimate injectivity accurately, in the absence of extraordinarily fine grid resolution near the injection well.