  We study two-loop Euler-Heisenberg effective actions in three-dimensional N=2
and N=4 supersymmetric quantum electrodynamics (SQED) without Chern-Simons
term. We find exact expressions for propagators of chiral superfields
interacting with slowly-varying N=2 gauge superfield. Using these propagators
we compute two-loop effective actions in the N=2 and N=4 SQED as the
functionals of superfield strengths and their covariant spinor derivatives. The
obtained effective actions contain new terms having no four-dimensional
analogs. As an application, we find two-loop quantum corrections to the moduli
space metric in the N=2 SQED.
