  Neutralino dark matter can be indirectly detected by observing the gamma ray
lines from the annihilation processes XX-->gg and XX-->gZ. In this paper we
study the implications that the observation of these two lines could have for
the determination of the supersymmetric parameter space. Within the minimal
supergravity framework, we find that, independently of the dark matter
distribution in the Galaxy, such observations by themselves would allow to
differentiate between the coannihilation region, the funnel region, and the
focus point region. As a result, several restrictions on the msugra parameters
can be derived. Within a more general MSSM scenario, we show that the
observation of gamma-ray lines might be used to discriminate between a bino-, a
wino-, and a higgsino-like neutralino, with important consequences for
cosmology and for models of supersymmetry breaking. The detection of the gamma
ray lines, therefore, will not only provide an unmistakable signature of dark
matter, it will also open a new road toward the determination of supersymmetric
parameters.
