The cosmon model for an asymptotically vanishing time-dependent cosmological ``constant''

We investigate the coupled system of gravity and a scalar with exponential potential. The energy momentum tensor of the scalar field induces a time-dependent cosmological ``constant''. This adjusts itself dynamically to become in the ``late'' universe (including today) proportional to the energy density of matter and radiation. Possible consequences for the present cosmology are shortly discussed. We also address the question of naturalness of the cosmon model.