  The screening properties of fullerene molecules are described by means of a
continuum model which uses the electronic wavefunctions of planar graphite as a
starting point. The long distance behavior of the system gives rise to a
renormalizable theory, which flows towards a non trivial fixed point. Its
existence implies an anomalous dielectric constant. The screening properties
are neither metallic nor insulating. Alternatively, the intramolecular
screening is obtained from a simple approximation to the electronic
wavefunctions. Intermolecular effects are also calculated. As a consistency
check, it is shown that the observed polarizability of C$_{60}$ is well
eproduced.
