In the statistical estimation theory, 
sufficient conditions for admissibility of estimators 
have been discussed mostly under quadratic loss function. 
Recently, under the LINEX loss function, sufficient conditions 
were developed in some families of distributions. 
However, they do not include some typical non-regular distributions 
so that the dimension of the minimal sufficient statistic is two. 
The purpose of this paper is to give 
sufficient conditions for admissibility of estimators 
in such non-regular distributions under the LINEX loss function. 
Some examples are also given.