q -polynomials can be defined for all the possible parameters, but their orthogonality properties are unknown for several configurations of the parameters. Indeed, orthogonality for the Askey–Wilson polynomials, p n ( x ; a , b , c , d ; q ) , is known only when the product of any two parameters a , b , c , d is not a negative integer power of q . Also, the orthogonality of the big q -Jacobi, p n ( x ; a , b , c ; q ) , is known when a , b , c , a b c − 1 is not a negative integer power of q . In this paper, we obtain orthogonality properties for the Askey–Wilson polynomials and the big q -Jacobi polynomials for the rest of the parameters and for all n ∈ N 0 . For a few values of such parameters, the three-term recurrence relation (TTRR) x p n = p n + 1 + β n p n + γ n p n − 1 , n ≥ 0 , presents some index for which the coefficient γ n = 0 , and hence Favard’s theorem cannot be applied. For this purpose, we state a degenerate version of Favard’s theorem, which is valid for all sequences of polynomials satisfying a TTRR even when some coefficient γ n vanishes, i.e., { n : γ n = 0 } ≠ 0̸ . We also apply this result to the continuous dual q -Hahn, big q -Laguerre, q -Meixner, and little q -Jacobi polynomials, although it is also applicable to any family of orthogonal polynomials, in particular the classical orthogonal polynomials.