  A new characterization of the generalized Hermite polynomials and of the
orthogonal polynomials with respect to the maesure $|x|^\g (1-x^2)^{\a-1/2}dx$
is derived which is based on a "reversing property" of the coefficients in the
corresponding recurrence formulas and does not use the representation in terms
of generalized Laguerre and Jacobi polynomials. A similar characterization can
be obtained for a generalization of the sieved ultraspherical polynomials of
the first and second kind. These results are applied in order to determine the
asymptotic limit distribution for the zeros when the degree and the parameters
tend to infinity with the same order.
