We discuss the general GAOR type (GGAOR) iterative method, of which special cases are the AOR, the GAOR, and the MSOR iterative methods, to solve the linear system Ax = b where A = I - L - U with L and U being general matrices. The GGAOR iteration matrix is expressed by L R Ω = (I - RL) - 1 [(I - Ω) + (Ω - R)L + ΩU] where R and Ω are diagonal matrices, and the MSOR iteration matrixL ω ω = (I - Ω) - 1 (I - Ω + ΩU). Some basic results on the upper bounds of the spectral radii ρ(L R Ω ) and ρ(L ω ω ) are given when A is strictly or irreducibly diagonally dominant by rows. Based upon these results, we obtain new results on the convergence regions of the GGAOR and the MSOR iterative methods when A is anH -matrix or A has property A, and recover and improve previous ones.