For the case 1 < p < ∞, 1 ≤ q ≤ ∞, 1/p < α < 1, r ≥ 0, we completely describe the set of outer functions, in the sense of the Nevanlinna factorization, for the analytic O. V. Besov classes AB_pq^r+α. Corollaries that are of the type of Λ^α/2-theorems are obtained.