The aim of this paper is to establish the convergence of the block iteration methods such as the block successively accelerated over-relaxation method (BAOR) and the symmetric block successively accelerated over-relaxation method (BSAOR): Let A∈ Cm,m π,n be a weak block H-matrix to partition π, then for 0≤r≤2/1+p(اB1+(A1ا)•p(Br.w)≤/1-w/(اB1+(A1ا)、P(BJ, r.w)≤[1-w]+wp(اB1+(A1ا)2and exact convergence and divergence domains for the block SOR and block SSOR iterative methods are obtained as it has been obtained to H-matrices. Based on these results, the main results in Bai [Parallel Computing 25 (1999)] and Cvetkovi´c [Appl. Numer. Math. 41 (2002)] can be improved.