We study tie scattering and blowup problem for a class of nonlinear Schrodinger equations with general nonlinearities in the spirit of Kenig and Merle [17]. Our conditions on the nonlinearities allow us to treat a wider class of those than ever treated by several authors, so that we can prove the existence of a ground state (a standing-wave solution of minimal action) for my frequency omega > 0. Once we get a ground state, a so-called potencial-well scenario works well: for the nonlinear dynamics determined by the nonlinear Schrodinger equations, we define two invariant regions A(omega,+) and A(omega,-) for each omega > 0 in H-1(R-d) such that any solution starting fro la A,+ behaves asymptotically free as t -> +/-infinity, one from A(omega,-) blows up or grows up, and the ground state belongs to (A(omega,+)) over bar boolean AND(A(omega,-)) over bar. Our weaker assumptions as to the nonlinearities demand that we argue in a subtle way in proving the crucial properties of the solutions in the invariant regions.