  In these notes we investigate the cone of nef curves of projective varieties,
which is the dual cone to the cone of pseudo-effective divisors. We prove a
structure theorem for the cone of nef curves of projective $\mathbb
Q$-factorial klt pairs of arbitrary dimension from the point of view of the
Minimal Model Program. This is a generalization of Batyrev's structure theorem
for the cone of nef curves of projective terminal threefolds.
