  Two sets of infinitely many exceptional orthogonal polynomials related to the
Wilson and Askey-Wilson polynomials are presented. They are derived as the
eigenfunctions of shape invariant and thus exactly solvable quantum mechanical
Hamiltonians, which are deformations of those for the Wilson and Askey-Wilson
polynomials in terms of a degree \ell (\ell=1,2,...) eigenpolynomial. These
polynomials are exceptional in the sense that they start from degree \ell\ge1
and thus not constrained by any generalisation of Bochner's theorem.
