  This work reports a theoretical study of the x-ray absorption near-edge
structure spectra at both the Cu and the Mn K-edge in several Cu$_2$MnM (M= Al,
Sn and In) Heusler alloys. Our results show that {\it ab-initio} single-channel
multiple-scattering calculations are able of reproducing the experimental
spectra. Moreover, an extensive discussion is presented concerning the role of
the final state potential needed to reproduce the experimental data of these
half-metallic alloys. In particular, the effects of the cluster-size and of the
exchange and correlation potential needed in reproducing all the experimental
XANES features are discussed.
