  Lead fluoride (PbF$_2$) crystals represent an excellent and relatively
innovative choice for high resolution electromagnetic calorimeters with high
granularity and fast timing for high intensity environments. For this reason
two PbF$_2$ crystals, sized $5\times 5 \times 40 $ mm$^3$, were irradiated with
$^{60}$Co photons up to $\sim 4$ Mrad and with 14 MeV neutrons up to a
$10^{13}$ n/cm$^2$ total fluence. Their loss in transmittance was evaluated at
different steps of the photon and neutron irradiation campaign, resulting in a
total of 30% loss above 350 nm. With crystals always kept in dark conditions,
natural and thermal annealing, as well as optical bleaching with 400 nm light,
were performed on the irradiated specimens, resulting in a partial recovery of
their original optical characteristics.
