  Let M_g be the moduli space of smooth curves of genus g >= 3, and \bar{M}_g
the Deligne-Mumford compactification in terms of stable curves. Let
\bar{M}_g^{[1]} be an open set of \bar{M}_g consisting of stable curves of
genus g with one node at most. In this paper, we determine the necessary and
sufficient condition to guarantee that a Q-divisor D on \bar{M}_g is nef over
\bar{M}_g^{[1]}, that is, (D . C) >= 0 for all irreducible curves C on
\bar{M}_g with C \cap \bar{M}_g^{[1]} \not= \emptyset.
