  The understanding of an electron gas with short coherence length pairs formed
by an attractive interaction is believed to be one of the major keys to our
theoretical knowledge of the high-T_c-superconductors. Mainly the deviations of
the cuprates from usual metallic Fermi liquid behaviour already in the normal
state like e.g. a linear resistivity or the observation of a pseudo gap can
result from electron-electron correlations.
  We therefore investigate the negative U Hubbard model in two dimensions at
low densities using the T-matrix approximation. In the non selfconsistent
formulation of the theory the system always shows an instability towards Bose
condensation of pairs into an infinite lifetime two-particle bound state. If
the calculations are performed selfconsistently pair-pair scattering is
included which causes the pairs to have finite lifetime. The physics of these
finite lifetime pairs is discussed.
