  We compute two-loop low-energy effective actions in Abelian Chern-Simons
matter models with N=2 and N=3 supersymmetry up to four-derivative order.
Calculations are performed with a slowly-varying gauge superfield background.
Though the gauge superfield propagator depends on the gauge fixing parameter,
it is shown that the obtained results are independent of this parameter. In the
massless case the considered models are superconformal. We demonstrate that the
superconformal symmetry strongly restricts the form of two-loop quantum
corrections to the effective actions such that the obtained terms have simpler
structure than the analogous ones in the effective action of three-dimensional
supersymmetric electrodynamics (SQED) with vanishing topological mass.
