We have studied the four-fermion processes ee → eeee, eeμμ, eeττ, μμμμ, μμττ, eeqq and μμqq with the L3 detector at LEP. For an integrated luminosity of 36 pb−, corresponding to 960 000 hadronic Z decays, we find a total of 67 candidate events. The rate and kinematical distributions are found to be consistent with first order Monte Carlo calculations based on the Standard Model. No significant structure is seen in the dilepton invariant or recoil mass spectra.