In this work we study the Glauber dynamics of the one-dimensional Ising model with nearest. neighbor and next-nearest-neighbor interactions，for which an approximate solution of the magnetiza-tion per site is obtained. When the dynamical critical exponent z is investigated following the treatment of Cordery，Sarker，and Tobochnik [Phys. Rev, B 24, 5402 (1981)], our observation shows that its upper. bound value is the same as the known value, thus implying that z is independent of the range of the in-teraction. We also suggest a high-temperature expansion approximation which is then used to solve the two-dimensional Glauber dynamics governed by a master equation; this solution is compared with that of the decoupling method. the time-delayed correlation function 1S also calculated.