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Two searches for supersymmetric particles in final states containing a same-flavour opposite-sign lepton pair, jets and large missing transverse momentum are presented. The proton–proton collision data used in these searches were collected at a centre-of-mass energy \(\sqrt {s}\) = 8 TeV by the ATLAS detector at the Large Hadron Collider and corresponds to an integrated luminosity of 20.3 fb\(^{−1}\). Two leptonic production mechanisms are considered: decays of squarks and gluinos with Z bosons in the final state, resulting in a peak in the dilepton invariant mass distribution around the Z-boson mass; and decays of neutralinos (e.g. \(\tilde{χ}\)\(^{0}_{2}\) → ℓ\(^{+}\)ℓ\(^{−}\)\(\tilde{χ}\)\(^{0}_{1}\)), resulting in a kinematic endpoint in the dilepton invariant mass distribution. For the former, an excess of events above the expected Standard Model background is observed, with a significance of three standard deviations. In the latter case, the data are well-described by the expected Standard Model background. The results from each channel are interpreted in the context of several supersymmetric models involving the production of squarks and gluinos.