  I review the approach [1] to the one-loop low-energy effective action in the
hypermultiplet sector for N=2 superconformal models. Any such a model contains
an N=2 vector multiplet and some number of hypermultiplets. We found a general
expression for the low-energy effective action in the form of a proper-time
integral. The leading space-time dependent contributions to the effective
action are derived and their bosonic component structure is analyzed. The
component action contains terms with three and four space-time derivatives of
component fields and has the Chern-Simons-like form.
