The β-assumed-p.d.f. approximation of Cook & Riley (1994) is tested as a subgrid model for the LES computation of non-premixed turbulent reacting flows, in the limit of infinitely fast chemistry, for two plane constant-density turbulent mixing layers with different degrees of intermittency. Excellent results are obtained in the computation of plane-averaged properties, such as product mass fractions and relatively high powers of the temperature, and even of the p.d.f. of the conserved scalar itself. In all these cases the errors are small enough to be useful in practical applications. The analysis is extended to slightly out-of-equilibrium problems, such as the generation of radicals, and formulated in terms of the p.d.f. of the gradient of the mixture fraction. It is shown that the form of the conditional gradient distribution is universal in a wide range of cases, whose limits are established. Within those limits, engineering approximations to the radical concentration are also possible. It is argued that the experiments in this paper are already in the limit of high Reynolds numbers.