  Let $M$ be an $n$-dimensional complex manifold. A holomorphic function
$f:M\to \mathbb C$ is said to be semi-Bloch if for every $\lambda\in \mathbb C$
the function $g_\lambda=\exp(\lambda f(z))$ is normal on $M$. We characterise
Semi-Bloch functions on infinitesimally Kobayashi non-degenerate $M$ in
geometric as well as analytic terms. Moreover, we show that on such manifolds,
semi-Bloch functions are normal.
