We study well-posedness of the initial value problem for the generalized Benjamin-Ono equation∂tu+uk∂xu−∂xDxu=0{\partial _t}u + {u^k}{\partial _x}u - {\partial _x}{D_x}u = 0,k∈Z+k \in {\mathbb {Z}^ + }, in Sobolev spacesHs(R){H^s}(\mathbb {R}). For small data and higher nonlinearities(k≥2)(k \geq 2)new local and global (including scattering) results are established. Our method of proof is quite general. It combines several estimates concerning the associated linear problem with the contraction principle. Hence it applies to other dispersive models. In particular, it allows us to extend the results for the generalized Benjamin-Ono to nonlinear Schrödinger equations (or systems) of the form∂tu−i∂x2u+P(u,∂xu,u¯,∂xu¯)=0{\partial _t}u - i\partial _x^2u + P(u,{\partial _x}u,\bar u,{\partial _x}\bar u) = 0.