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.