This paper presents the numerical solution of sixth order Adams Bashforth-Moulton block method for solving neutral delay differential equations (NDDE) with the type of constant and time-dependent delay. There are two techniques that has been implemented in approximating the neutral delay term, y′(t-τ). First, at the starting point of the multistep block method, the neutral delay is approximated by using initial function or extrapolation. Meanwhile, in the block method itself seven points of stored values has been used to approximate this term using Newton divided difference interpolation with the variable step size strategy. Some of the mathematical problems has been tested and implemented using Visual C programming. Numerical results show that the proposed method is reliable and efficient when compared with the other methods.
