Abstract: The problem of linear hypothesis testing of the multivariate normal linear model Y-N_n×m (XB, I_n⊗∑) is considered under the normal-inverse Wishart prior distribution of the parameter matrices (B,∑). Two posterior likelihood ratio tests for the linear hypothesis about the parameter matrix B are constructed. The likelihood ratio statistics obtained from the posterior distribution of B are functions of the characteristic roots of the random matrices which have matric F-distribution.