This work discusses the state space exact linearization problems, both locally and globally, for single-input single-output nonlinear systems. First it is shown that if the input vector field has a particular structure, i.e. if it is a constant vector field, then local or global feedback linearizability can be determined by inspection. Then it is shown that, under mild assumptions, there always exists a suitable (local) coordinates transformatrion which transforms a general nonlinear plant into a system with constant input vector. Using these two facts, simple conditions for local and global feedback linearizability of SISO nonlinear systems are derived. Finally, an explicit formula to locally rectify an affine vector field is presented.