  We study the local classification of higher order Fuchsian linear
differential equations under various refinements of the classical notion of the
"type of differential equation" introduced by Frobenius. The main source of
difficulties is the fact that there is no natural group action generating this
classification.
  We establish a number of results on higher order equations which are similar
but not completely parallel to the known results on local (holomorphic and
meromorphic) gauge equivalence of systems of first order equations.
