  We generalize results of Hattori on the topology of complements of hyperplane
arrangements, from the class of generic arrangements, to the much broader class
of hypersolvable arrangements. We show that the higher homotopy groups of the
complement vanish in a certain combinatorially determined range, and we give an
explicit Z\pi_1-module presentation of \pi_p, the first non-vanishing higher
homotopy group. We also give a combinatorial formula for the \pi_1-coinvariants
of \pi_p.
  For affine line arrangements whose cones are hypersolvable, we provide a
minimal resolution of \pi_2, and study some of the properties of this module.
For graphic arrangements associated to graphs with no 3-cycles, we obtain
information on \pi_2, directly from the graph. The \pi_1-coinvariants of \pi_2
may distinguish the homotopy 2-types of arrangement complements with the same
\pi_1, and the same Betti numbers in low degrees.
