  We study the class of transitive skew-products associated with iterated
function systems of circle diffeomorphisms. We can approximate any transitive
skew-product by maps in this class that have a robustly zero Lyapunov exponent.
In particular, we prove the existence of non-hyperbolic ergodic measures for an
open and dense subset of transitive skew-products. Moreover, these measures
have full support and are the weak$^*$ limit of periodic measures.
