  We introduce a natural generalisation of holomorphic curves to morphisms of
supermanifolds, referred to as holomorphic supercurves. More precisely,
supercurves are morphisms from a Riemann surface, endowed with the structure of
a supermanifold which is induced by a holomorphic line bundle, to an ordinary
almost complex manifold. They are called holomorphic if a generalised
Cauchy-Riemann condition is satisfied. We show, by means of an action identity,
that holomorphic supercurves are special extrema of a supersymmetric action
functional.
