The invention relates to a synergistic mixture comprising: a) at least one compound selected from the group consisting of the phosphites of the formula (I) to (V), of the phosphonites of the formulae (VI) to (IX) and (XV), of the di/oligophosphonites of the formulae (X) and (XI) and of the phosphinites of the formulae (XII) to (XIV); and b) at least one compound selected from the group consisting of the phosphanes of the formula (XVI), the di/oligophosphanes of the formulae (XVII) and (XVIII), and of the cyclophosphanes of the formula (XIX),and also to a process for stabilizing polymers with respect to thermooxidative degradation by addition and incorporation of a synergistic mixture of this type.