The DELPHI experiment at the LEP e + e- collider collected almost 700 pb-1 at centre-of-mass energies above the Z0 mass pole and up to 208 GeV. Those data were used to search for SUSY in the Anomaly Mediated SUSY Breaking (AMSB) scenario with a flavour independent common sfermion mass parameter. The searches covered several possible signatures experimentally accessible at LEP, with either the neutralino, the sneutrino or the stau being the Lightest Supersymmetric Particle (LSP). They included: the search for nearly mass-degenerate chargino and neutralino, which is a typical feature of AMSB; the search for Standard-Model-like or invisibly decaying Higgs boson; the search for stable staus; the search for cascade decays of SUSY particles resulting in the LSP and a low multiplicity final state containing neutrinos. No evidence of a signal was found, and thus constraints were set in the space of the parameters of the model.