  We consider the leading and subleading UV divergences for the four-point
on-shell scattering amplitudes in D=8 N=1 sypersymmetric Yang-Mills theory
within the spinor-helicity and superfield formalism. This theory belongs to the
class of maximally supersymmetric gauge theories and presumably possesses
distinguished properties beyond perturbation theory. We obtain the recursive
relations that allow one to get the leading and subleading divergences in all
loops in a pure algebraic way staring from the one loop (for the leading poles)
and two loop (for the subleading ones) diagrams. As a particular example where
the recursive relations have a simple form we consider the ladder type
diagrams. The all loop summation of the leading and subleading divergences is
performed with the help of the differential equations which are the
generalization of the RG equations for non-renormalizable theories. They have
explicit solutions for the ladder type diagrams. We discuss the properties of
the obtained solutions and interpretation of the results.
