We investigate the behaviour of weak ferromagnetic metals close to the
ferromagnetic critical point. We show that in the limit of small magn
etic moment the low temperature metallic phase is rigorously described
by a local ferromagnetic Fermi liquid that has a momentum-independent
self-energy. Whereas, non-Fermi liquid features develop at higher tem
peratures. Furthermore, we find that an instability towards s-wave sup
erconductivity is possible when the exchange splitting is comparable t
o the superconducting gap.