  This paper provides a framework to strong time periodic solutions of
quasilinear evolution equations. The novelty of this approach is that zero is
allowed to be a spectral value of the underlying linearized operator. This
approach is then applied to time periodic problems associated to the
Navier-Stokes equations, generalized Newtonian fluids, quasilinear
reaction-diffusion systems as well as to magneto-hydrodynamics.
