This article brings an approximation theorem for sections of Oka pairs of sheaves of homogeneous spaces (such sheaves were introduced in [15]). Among the applications are: an Oka principle for the approximation of a generating system for a coherent analytic sheaf and an Oka principle for the approximation of a holomorphic fibre bundle with homogeneous fibre (without a structure group). Together with a homotopy theorem [15] for Oka pairs of sheaves of homogeneous spaces, a theoretical unification is thus given for various known results on the Oka principle [12,20,6,7].