  On a complex curve, we establish a correspondence between integrable
connections with irregular singularities, and Higgs bundles such that the Higgs
field is meromorphic with poles of any order.
  The moduli spaces of these objects are obtained by fixing at each singularity
the polar part of the connection. We prove that they carry hyperKahler metrics,
which are complete when the residue of the connection if semisimple.
