  We show a method to construct isospectral deformations of classical
orthogonal polynomials. The construction is based on confluent Darboux
transformations, and it allows to construct Sturm-Liouville problems with
polynomial eigenfunctions that have an arbitrary number of continuous
parameters. We propose to call these new orthogonal polynomial systems
\emph{exceptional polynomials of the second kind}. We illustrate this
construction by describing the class of exceptional Gegenbauer polynomials of
the second kind.
