Abstract: The limit distribution of the log maximum likelihood ratio statistic for finite mixture models is not the usual chisqure （Hartigan 1985）. We have considered the limit distribution of the restricted log maximum likehood ratio for mixture models of two distributions with single unknown parameter 2. But it does not contain mixture models of two useful normal distribution with unknown mean and variance, it has another limit distribution. In this papaer, we give this limit distribution and its tables of values.