**MSC:**- 62F07 Ranking and selection
- 62F35 Robustness and adaptive procedures

parameter set the asymptotic behavior of the maximum risk is

studied for the problem of classification into disjoint subsets.

The exponential rates of the optimal decision rule is determined

and expressed in terms of the normalized limit of moment

generating functions of likelihood ratios. Necessary and

sufficient conditions for the existence of adaptive

classification rules in the sense of Rukhin [10] are given. The

results are applied to the problem of the selecting of the best

population. Exponential families are studied as a special case,

and an example for the normal case is included.