Results are presented of a study on the degradation of the electrical and optical performance of n+p Si avalanche photodiodes, subjected to 1-MeV fast neutrons and to a 220-MeV carbon irradiation. The dark current increases after irradiation, while the photo current decreases. Two dominant hole capture levels, which are responsible for the degradation of performance, are after irradiation observed by DLTS (Deep Level Transient Spectroscopy). The degradation caused by neutron irradiation is smaller than that for carbon irradiation. The differences in the radiation damage are explained by the differences in the number of knock-on atoms and the nonionizing energy loss (NIEL). The recovery behavior of the device performance by isochronal annealing is also reported.