Approximately 438 pb^-1 of e+e- data from the OPAL detector, taken with the LEP collider running at centre-of-mass energies of 192-209 GeV, are analyzed to search for evidence of chargino pair production, e+e- --> chi+_1 chi-_1, or neutralino associated production, e+e- --> chi0_2 chi0_1. Limits are set at the 95% confidence level on the product of the cross-section for the process e+e- --> chi+_1 chi-_1 and its branching ratios to topologies containing jets and missing energy, or jets with a lepton and missing energy, and on the product of the cross-section for e+e- --> chi0_2 chi0_1 and its branching ratio to jets. R-parity conservation is assumed throughout this paper. When these results are interpreted in the context of the Constrained Minimal Supersymmetric Standard Model, limits are also set on the masses of the chi+-_1, chi0_1 and chi0_2, and regions of the parameter space of the model are ruled out. Nearly model-independent limits are also set at the 95% confidence level on sigma(e+e- --> chi+_1 chi-_1) with the assumption that each chargino decays via a W boson, and on sigma(e+e- --> chi0_2 chi0_1) with the chi0_2 assumed to decay via a Z0.