  A projective log variety (X, D) is called "a log Fano manifold" if X is
smooth and if D is a reduced simple normal crossing divisor on X with -(K_X+D)
ample. The n-dimensional log Fano manifolds (X, D) with nonzero D are
classified in this article when the log Fano index r of (X, D) satisfies either
r\geq n/2 with \rho(X)\geq 2 or r\geq n-2. This result is a partial
generalization of the classification of logarithmic Fano threefolds by Maeda.
