Let R be a prime ring of characteristic different from 2 with the center Z(R) and F , G be b-generalized skew derivations on R. Let U be Utumi quotient ring of R with the extended centroid C and f (x 1 , . . . , x n ) be a multilinear polynomial over C which is not central valued on R. Suppose that P / ∈ Z(R) such thatfor all r = (r 1 , . . . , r n ) ∈ R n , then one of the following holds:(1) there exist λ, µ ∈ C such that F (x) = λx, G(x) = µx for all x ∈ R;(2) there exist a, b ∈ U , λ, µ ∈ C such that F (x) = ax+λx+xa, G(x) = bx+µx+xb for all x ∈ R and f (x 1 , . . . , x n ) 2 is central valued on R.