The purpose of this paper is to show that three possible characterizations of the notion of "transmission zero", namely "pole" of the inverse system, zero-output-constrained dynamics and unobservable dynamics under certain state-feedback, which are equivalent for any invertible linear system, may have different analogues for nonlinear input-affine systems. It is also shown that some nonlinear versions of the so-called structure algorithm, proposed by Hirschorn and Singh, may be successfully used in this framework.