Recent results on the short-time behaviors of a few models possessing a common feature of long-ranged interaction will be summarized. For the disorder initial state, the initial order increase is observed for each model in a heat-bath at the critical temperature. The dynamic exponents are calculated. For arbitrary initial order and environment temperature, universal characteristic functions are introduced in order to generalize the scaling relations. Remarkable consistence between the theoretic renormalization group results and the simulations are found in the long-range regime.