  We derive the actions for type II Green-Schwarz strings up to second order in
the fermions, for general bosonic backgrounds. We base our work on the
so-called normal coordinate expansion. The resulting actions are
$\kappa$-symmetric and, for the case of surviving background supersymmetries,
supersymmetric. We first obtain the type IIa superstring action from the 11D
supermembrane by double dimensional reduction. Then, by means of a
generalization of T-duality we derive the type IIb superstring action. The
resulting actions are surprisingly simple and elegant.
