Abstract: For k-step-ahead predictors of ARMAX model both single-step and multi-step forms are reviewed. The singlestep formulation depends on several past values of fixed step(k-step) predictors, while the rnultistep form uses multiple recursivity of different step (k-l-step k-2-step, ....) predictors at fixed time. In this paper the equivalence relation of two forms is established, in a addition, the comparison of them from the viewpoint of application and simulation results is given.