  The work proposes a geometric background of the theory of field interactions
and strings in spaces with higher order anisotropy. Our approach proceeds by
developing the concept of higher order anisotropic superspace which unifies the
logical and mathematical aspects of modern Kaluza-Klein theories and
generalized Lagrange and Finsler geometry and leads to modelling of physical
processes on higher order fiber bundles provided with nonlinear and
distingushed connections and metric structures. The view adopted is that a
general field theory should incorporate all possible anisotropic and stochastic
manifestations of classical and quantum interactions and, in consequence, a
corresponding modification of basic principles and mathematical methods in
formulation of physical theories. The presentation is divided into two parts.
The first five sections cover the higher order anisotropic superspaces. We
focus on the geometry of distinguished by nonlinear connection vector
superbundles, consider different supersymmetric extensions of Finsler and
Lagrange spaces and analyze the structure of basic geometric objects on such
superspaces. The remaining five sections are devoted to the theory of higher
order anisotropic superstrings. In the framework of supersymmetric nonlinear
sigma models in Finser extended backgrounds we prove that the low-energy
dynamics of such strings contains motion equations for locally anisotropic
field interactions.
