  Generalized Weierstrass formulae for surfaces in four-dimensional space
$\Bbb{R}^{4}$ are used to study (anti)self-dual rigid string configurations. It
is shown that such configurations are given by superminimal immersions into
$\Bbb{R}^{4}$. Explicit formulae for generic (anti)instantons are presented.
Particular classes of surfaces are also analyzed.
