Scalar partners of quarks and leptons, predicted in supersymmetric models, are searched for in e+e− collisions at centre-of-mass energies between 192 and 209 GeV at LEP. No evidence for any such particle is found in a data sample of 450 pb−1. Upper limits on their production cross sections are set and lower limits on their masses are derived in the framework of the Minimal Supersymmetric Standard Model.