I will report the work by Gongyo and Lehmann on connection between nef reduction and minimal models. Consider a pair (X, D) and morphism f: X ->Z. Suppose that the restriction of K_X+D on the general fiber F has numerical dimension 0. I will report on the connection between the existence of a good minimal model of (X, D) and the existence of a good minimal model of (Z', D'), where Z' is a suitable modification of Z.