  In this paper we show that the only sequences of orthogonal polynomials
$(P_n)_{n\geq 0}$ satisfying \begin{align*} \phi(x)\mathcal{D}_q
P_{n}(x)=a_n\mathcal{S}_q P_{n+1}(x) +b_n\mathcal{S}_q P_n(x) +c_n\mathcal{S}_q
P_{n-1}(x), \end{align*} ($c_n\neq 0$) where $\phi$ is a well chosen polynomial
of degree at most two, $\mathcal{D}_q$ is the Askey-Wilson operator and
$\mathcal{S}_q$ the averaging operator, are the multiple of Askey-Wilson
polynomials, or specific or limiting cases of them.
