  It is well-known that molecular dynamics integrators, which are used for
lattice quantum chromodynamics (QCD), suffer from instabilities and possess a
rather low order of the accuracy. Hence, it is highly desirable to construct a
new class of geometric integrators, that overcomes these instability problems
and increases the order of accuracy without increasing remarkably the
computational costs.
  In this paper we consider for this purpose multistep methods and give an
overview of known results to systematize important knowledge for such methods
being the right choice for lattice QCD simulations. At the end we try to answer
the question: can multistep method be used as molecular dynamic integrators and
what might be the advantage of it.
