  We define and study a natural system of tautological rings on the moduli
spaces of marked curves at the level of differential forms. We show that
certain 2-forms obtained from the natural normal functions on these moduli
spaces are tautological. Also we show that rings of tautological forms are
always finite dimensional. Finally we characterize the Kawazumi-Zhang invariant
as essentially the only smooth function on the moduli space of curves whose
Levi form is a tautological form.
