  An interesting discovery in the last two years in the field of mathematical
physics has been the exceptional $X_\ell$ Laguerre and Jacobi polynomials.
Unlike the well-known classical orthogonal polynomials which start with
constant terms, these new polynomials have the lowest degree $\ell=1,2,...$,
and yet they form complete sets with respect to some positive-definite measure.
In this paper, we study one important aspect of these new polynomials, namely,
the behaviors of their zeros as some parameters of the Hamiltonians change.
