The Nikolskii-Besov spaces B pq α ( R n )≡ B pq α , 1≤ p, q≤∞ , α>0 , recently were described using the Caputo's fractional derivative. Using the concept of weak fractional derivative, in this paper we reduces the characterization of B pq α to the case B pq γ , where γ is any positive number strictly less than α .