A fundamental problem in plasma and astrophysics is the interaction between magnetic turbulence and charged particles such as cosmic rays. Those particles experience different scattering effects. The most important are spatial diffusion along and across a mean magnetic field. In this paper an improved nonlinear guiding center theory for cross-field scattering is discussed in more detail than before. Furthermore, the theory is extended to allow dynamical and non-axisymmetric turbulence.