  We study a rational version of the double affine Hecke algebra associated to
the nonreduced affine root system of type $(C^\vee_n,C_n)$. A certain
representation in terms of difference-reflection operators naturally leads to
the definition of nonsymmetric versions of the multivariable Wilson
polynomials. Using the degenerate Hecke algebra we derive several properties,
such as orthogonality relations and quadratic norms, for the nonsymmetric and
symmetric multivariable Wilson polynomials.
