In supersymmetric models where the gravitino is the lightest superparticle, the next-to-lightest superparticle (NLSP) is long-lived, and hence could be collected and studied in detail. We study the prospects of direct detection of lepton flavour violation in charged slepton NLSP decays. Mixing angles in the slepton sector as small as ∼ 3 × 10⁻² (9 × 10⁻³) could be probed at the 90 confidence level if 3 × 10³ (3 × 10⁴) sleptons could be collected.