Many mathematicians in ([1], [2], [5], [14], [20]) introduced and investigated the generalized q-Bernoulli numbers and polynomials and the generalized q-Euler numbers and polynomials and the generalized q-Gennochi numbers and polynomials. Mahmudov ([15], [16]) considered and investigated the q-Bernoulli polynomials B (α) n,q x, y in x, y of order α and the q-Euler polynomials E (α) n,q x, y in x, y of order α. In this work, we define generalized q-poly-Bernoulli polynomials B [k,α] n,q x, y in x, y of order α. We give new relations between the generalized q-poly-Bernoulli polynomials B [k,α] n,q x, y in x, y of order α and the generalized q-poly-Euler polynomials E [k,α] n,q x, y in x, y of order α and the q-Stirling numbers of the second kind S 2,q (n, k)