  Limiting cases are studied of the Koornwinder-Macdonald multivariable
generalization of the Askey-Wilson polynomials. We recover recently and not so
recently introduced families of hypergeometric orthogonal polynomials in
several variables consisting of multivariable Wilson, continuous Hahn and
Jacobi type polynomials, respectively. For each class of polynomials we provide
systems of difference (or differential) equations, recurrence relations, and
expressions for the norms of the polynomials in terms of the norm of the
constant polynomial.
