This paper presents theorems which can be used to obtain sufficient and minimal sufficient statistics for the two-way classification mixed model design. Using the general linear hypothesis modelY=Xτ+Zβ+e the authors prove that the dimension of a minimal sufficient statistic is a function of the ranks of certain submatrices ofZ×X. Minimal sufficient statistics are presented in tabular form for some two-way classification designs and some of the distributional properties are given.