  A total of 628 pb-1 of data collected with the ALEPH detector at
centre-of-mass energies from 189 to 209 GeV is analysed in the search for gauge
mediated supersymmetry breaking (GMSB) topologies. In this framework, a novel
search for six-lepton final states when the stau is the next-to-lightest
supersymmetric particle (NLSP) and has negligible lifetime is performed. Other
possible signatures at LEP are studied and the ALEPH final results described
for two acoplanar photons, non-pointing single photons, acoplanar leptons,
large impact parameter leptons, detached slepton decay vertices, heavy stable
charged sleptons and multi-leptons plus missing energy final states. No
evidence is found for new phenomena, and lower limits on the masses of the
relevant supersymmetric particles are derived. A scan of a minimal GMSB
parameter space is performed and lower limits are set for the NLSP mass at 54
GeV and for the mass scale parameter Lambda at 10 TeV, independent of the NLSP
lifetime. Including the results from the neutral Higgs boson searches, a NLSP
mass limit of 77 GeV is obtained and values of Lambda up to 16 TeV are
excluded.
