Big q-Jacobi polynomials {P n (·; a, b, c; q)} ∞ n=0 are classically defined for 0 < a < q −1 , 0 < b < q −1 and c < 0. For the family of little q-Jacobi polynomials { p n (·; a, b|q)} ∞ n=0 , classical considerations restrict the parameters imposing 0 < a < q −1 and b < q −1 . In this work we extend both families in such a way that wider sets of parameters are allowed, and we establish orthogonality conditions for those cases for which Favard's theorem does not work. As a by-product, we obtain similar results for the families of big and little q-Laguerre polynomials.