  We study chaotic systems with multiple time delays that range over several
orders of magnitude. We show that the spectrum of Lyapunov exponents (LE) in
such systems possesses a hierarchical structure, with different parts scaling
with the different delays. This leads to different types of chaos, depending on
the scaling of the maximal LE. Our results are relevant, in particular, for the
synchronization properties of hierarchical networks (networks of networks)
where the nodes of subnetworks are coupled with shorter delays and couplings
between different subnetworks are realized with longer delay times. Units
within a subnetwork can synchronize if the maximal exponent scales with the
shorter delay, long range synchronization between different subnetworks is only
possible if the maximal exponent scales with the long delay. The results are
illustrated analytically for Bernoulli maps and numerically for tent maps.
