**MSC:**- 62F05 Asymptotic properties of tests
- 62F12 Asymptotic properties of estimators

Q_{\theta_1} and Q_{\theta_2} with unknown parameters \theta_1, \theta_2

\in H and let \pi_3 be a third population whose distribution Q_{\theta_3}

coincides with that of either \pi_1 or \pi_2. Assume there are given

samples of size n_1=n_2 and n_3, it is not to be decided whether

Q_{\theta_3}=Q_{\theta_1} or Q_{\theta_3}=Q_{\theta_2}. The desicion

problem is described by a sequence of localized experiments. The

corresponding lower Hajek-LeCam-bound is established and there is

constructed a sequence of decision rules based on ML-estimators which

attains this bound and is therefore considered to be asymptotic optimal.