We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic fourth order nonlinear Schrödinger equation with initial data u0 ∈ X, where6 and s2 > 1 2 we show that the Cauchy problem is unconditionally wellposed in X. Similar results hold true for all higher order nonlinear Schrödinger equations and mixed order NLS due to a factorization property of the corresponding phase factors. For the proof we employ the normal form reduction via the differentiation by parts technique and build upon our previous work.