  We study the umbral "classical" orthogonal polynomials with respect to a
generalized derivative operator $\cal D$ which acts on monomials as ${\cal D}
x^n = \mu_n x^{n-1}$ with some coefficients $\mu_n$. Let $P_n(x)$ be a set of
orthogonal polynomials. Define the new polynomials $Q_n(x) =\mu_{n+1}^{-1}{\cal
D} P_{n+1}(x)$. We find necessary and sufficient conditions when the
polynomials $Q_n(x)$ will also be orthogonal. Apart from well known examples of
the classical orthogonal polynomials we present a new example of umbral
classical polynomials expressed in terms of elliptic functions.
