  The $X_1$-Jacobi and the $X_1$-Laguerre exceptional orthogonal polynomials
have been introduced and studied by G\'omez-Ullate, Kamran and Milson in a
series of papers. In this note, we establish some properties, such as
interlacing, monotonicity with respect to the parameters and order, about the
so-called \textit{regular} and \textit{exceptional} zeros of these two classes
of polynomials.
