  We study holomorphic supercurves, which are motivated by supergeometry as a
natural generalisation of holomorphic curves. We prove that, upon perturbing
the defining equations by making them depend on a connection, the corresponding
linearised operator is generically surjective. By this transversality result,
we show that the resulting moduli spaces are oriented finite dimensional smooth
manifolds. Finally, we examine how they depend on the choice of generic data.
