We impose a condition of pointwise convergence on the
Lyapunov exponents of a d-dimensional cocycle over a compact metric
minimal flow. This condition turns out to have significant consequences
for the dynamics of the cocycle. We make use of such classical ODE
techniques as the Lyapunov-Perron triangularization method, and the
ergodic-theoretical techniques of Krylov and Bogoliubov.
