A new model of gamma radiation (GR) generated by neutralino annihilati
on in neutralino stars (NeS) is proposed. Diffuse galactic and extraga
lactic GR is calculated for this model and is shown to be in reasonabl
e agreement with observations. The point-source component (P) is picke
d out among nonidentified discrete gamma sources from the EGRET catalo
g. This component is shown to be distributed isotropically and homogen
eously, as it should be for NeS. Gamma radiation from a significant pa
rt of P-sources is supposed to be the direct radiation from individual
NeS. This supposition is shown to be in agreement with observations.
The comparison of the theory with observed GR gives a possibility to e
stablish some important features of the CDM particle.