  A search for slepton production via the decay of pair-produced neutralinos
has been performed under the assumption that the sleptons have observable
lifetime in the detector before each decays to a lepton and a gravitino.
Sleptons, neutralinos and gravitinos are particles predicted by the theory of
supersymmetry, and are the supersymmetric partners of the Standard Model
leptons, neutral bosons and of the graviton respectively. The search was
performed in 628 inverse picobarns of data taken by the ALEPH detector at LEP
centre-of-mass energies from 189 to 208 GeV. It was motivated by general
predictions of Gauge-Mediated Supersymmetry Breaking (GMSB) models in which the
lightest supersymmetric particle is always the gravitino. No evidence of the
process was found. Model-independent cross-section limits are quoted as a
function of neutralino mass, slepton mass and slepton lifetime in the case that
the neutralino branching ratios to each slepton are equal at one third (the
so-called slepton co-NLSP scenario, where NLSP stands for `Next-to-Lightest
Supersymmetric Particle') and in the case that the neutralino decays
exclusively to the stau (the stau-NLSP scenario). Excluded regions in the
neutralino-stau mass plane are shown for four gravitino masses under
model-specific assumptions.
