The authors study the boundedness and asymptotic behavior of positive solutions of the system of difference equations \[ x_{n+1}=A+\frac{\sum_{i=1}^{k} a_ix_{n-p_i}}{\sum_{j=1}^{m}b_jy_{n-q_j}},\qquad y_{n+1}=B+\frac{\sum_{i=1}^{k} c_iy_{n-p_i}}{\sum_{j=1}^{m}d_jx_{n-q_j}}, \] and obtain some results, where \(k, m\in \{1, 2, \ldots\}, A, B, a_i, c_i, b_j, d_j,\;i\in \{1, \ldots, k\},\;j\in \{1, \ldots, m\}\), are positive constants, \(p_i, q_j,\;i\in \{1, \ldots, k\},\;j\in \{1, \ldots, m\}\), are positive integers such that \(p_1