A search for chargino and neutralino pair production in e + e − collisions at center-of-mass energies between 161 GeV and 183 GeV is performed under the assumptions that R-parity is not conserved and that only purely leptonic or hadronic R-parity violating decays are allowed. No signal is found in the data. Limits on the production cross sections, on the Minimal Supersymmetric Standard Model parameters and on the masses of the supersymmetric particles are derived.