Data taken by the DELPHI experiment at centre-of-mass energies of 183 GeV and 189 GeV with a total integrated luminosity of 212 pb^{-1} have been used to search for the supersymmetric partners of the electrons, muons, and taus in the context of the Minimal Supersymmetric Standard Model (MSSM). The decay topologies searched for were the direct decay ({\tilde \ell} -> \ell {\tilde \chi_1^0}), producing acoplanar lepton pairs plus missing energy, and the cascade decay ({\tilde \ell} -> \ell {\tilde \chi_2^0} -> \ell \gamma {\tilde \chi_1^0}), producing acoplanar lepton and photon pairs plus missing energy. The observed number of events is in agreement with Standard Model predictions. The 95% CL excluded mass limits for selectrons, smuons and staus are m_{\tilde {e}} \leq 87 GeV/c^2, m_{\tilde {\mu}} \leq 80 GeV/c^2 and m_{\tilde {\tau}} \leq 75 GeV/c^2, respectively, for values of \mu=-200 GeV/c^2 and tan(beta)=1.5.