  Criteria for the simplicity of the Lyapunov spectra of linear cocycles have
been found by Furstenberg, Guivarc'h-Raugi, Gol'dsheid-Margulis and, more
recently, Bonatti-Viana and Avila-Viana. In all the cases, the authors consider
cocycles over hyperbolic systems, such as shift maps or Axiom A
diffeomorphisms.
  In this paper we propose to extend such criteria to situations where the base
map is just partially hyperbolic. This raises several new issues concerning,
among others, the recurrence of the holonomy maps and the (lack of) continuity
of the Rokhlin disintegrations of $u$-states.
  Our main results are stated for certain partially hyperbolic skew-products
whose iterates have bounded derivatives along center leaves. They allow us, in
particular, to exhibit non-trivial examples of stable simplicity in the
partially hyperbolic setting.
