  We study one-loop low-energy effective action in the hypermultiplet sector
for ${\cal N}=2$ superconformal models. Any such a model contains ${\cal N}=2$
vector multiplet and some number of hypermultiplets. Gauge group $G$ is assumed
to be broken down to $\tilde{G}\times K$ where $K$ is an Abelian subgroup and a
background vector multiplet belongs to the Cartan subalgebra corresponding to
$K$. We find a general expression for the low-energy effective action in a 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 the terms with three and four
space-time derivatives of component fields and has the Chern-Simons form.
