A nonlinear discriminant rule may be estimated by maximum likelihood estimation using unclassified observations. The performance of a nonlinear discriminant function based on a sample from a mixture of two Weibull distributions, with parameters λ, θ1, θ2 and p, is examined. Asymptotic expansion and asymptotic expected values of probabilities of misclassification are presented. The asymptotic relative efficiencies (AREs) of mixture and classified discrimination procedures are evaluated and discussed for selected parameters. Computations show that for fixed λ and p, as Δ = | θ1 − θ2| increases the ARE increases. Furthermore, for fixed λ and Δ, as p varies from 0.2 to 0.8 the values of ARE decrease. On the other hand, for fixed p and Δ, the ARE in case of λ = 0.5 are close to the ARE in the case of λ = 2.