  The concept of $\lambda$-differential operators is a natural generalization
of differential operators and difference operators. In this paper, we determine
the $\lambda$-differential Lie algebraic structure on the Witt algebra and the
Virasoro algebra for invertible $\lambda$. Then we consider several families of
modules over the Virasoro algebra with explicit module actions and determine
the $\lambda$-differential module structures on them.
