A systematic search has been made for events which appear to be due to the disintegration of a hyperfragment; that is, a nuclear fragment which contains a bound unstable particle. A total of 20 000 3-Bev proton stars and 500 1.5-Bev 7r~-meson stars from the Brookhaven Cosmotron were studied as well as 9000 cosmic-ray stars. Twenty-one events which are interpreted as hyperfragments were found in the proton plates, seven in the cosmic-ray plates and one in the x-meson plates. Of the 29 disintegrations, a x meson was ejected in only two cases and a iT-meson in one event. In the remaining 26 disintegrations, only nuclear particles were emitted. The charge and energy distributions, as well as the angular distribution of the hyperfragments, have been measured. In four cases the energetics of the decay strongly indicate that the bound unstable particle was a A 0 particle. The binding of the A 0 particle was measured in these cases. In two additional cases the minimum energy release was significantly greater than the decay energy of a A 0 particle but possibly consistent with the decay energy of a charged hyperon. In one case a negative iT-meson was ejected from a secondary star. It is impossible to determine whether this secondary star was due to a fragment disintegration or the nuclear capture of a stopped particle. This event cannot be explained in terms of established unstable particles.