  The fluxes of light antinuclei A<=4 induced near earth by Cosmic Ray intera
ctions with the interstellar matter in the Galaxy and with the Earth
atmosphere, are calculated in a phenomenological framework. The hadronic
production cross section for antinucleons is based on a recent parametrization
of a wide set of accelerator data. The production of light nuclei is calculated
using coalescence models. For the standard coalescence model, the coalescence
radius is fitted to the available experimental data. The non annihilating
inelastic scattering process for the antideuterons is discussed and taken into
account for the first time via a more realistic procedure than used so far for
antiprotons.
