Abstract： For two normal populations with unknown means μi and variancesσi2 ＞ 0, i= 1 , 2. Assume that there is a semi-order restriction between ratios ofmeans and standard deviations. A procedure of obtaining the maximum likelihoodestimators ofμi's and σi's under the semi-order restrictions is proposed. For i = 3case, some connected results are given. These methods are abroad applied in biologic-al inheritance and medicinal test.