We have searched for excited states of charged and neutral leptons, e * , μ * , τ * and ν * , in e + e - collisions at s = 161 GeV using the OPAL detector at LEP. No evidence for their existence was found. With the most common coupling assumptions, the topologies from excited lepton pair production include l + l - γγ andl + l - W + W - , with the subsequent decay of the virtual W bosons. From the analysis of these topologies, 95% confidence level lower mass limits of 79.9 GeV for e * , 80.0 GeV for μ * , 79.1 GeV for τ * , 78.3 GeV for ν * e , 78.9 GeV for ν * μ and 76.2 GeV for ν * τ are inferred. From the analysis of W + W - and γγ topologies with missing energy and using alternative coupling assignments which favour chargedl * ± and photonic ν * decays, 95% confidence level lower mass limits of 77.1 GeV for each l * ± flavour and 77.8 GeV for each ν * flavour are inferred. From the analysis of the l + l - γ,l ± W and single γ final states expected from excited lepton single production, upper limits on the ratio of the coupling to the compositeness scale, f/Λ, are determined for excited lepton masses up to the kinematic limit.