  If E is a flat bundle of rank r over a K\"ahler manifold X, we define the
Lyapunov spectrum of E: a set of r numbers controlling the growth of flat
sections of E, along Brownian trajectories. We show how to compute these
numbers, by using harmonic measures on the foliated space P(E). Then, in the
case where X is compact, we prove a general inequality relating the Lyapunov
exponents and the degrees of holomorphic subbundles of E and we discuss the
equality case.
