  The geometrical structure and the quantum properties of the recently proposed
harmonic space action describing self-dual Yang-Mills (SDYM) theory are
analyzed. The geometrical structure that is revealed is closely related to the
twistor construction of instanton solutions. The theory gets no quantum
corrections and, despite having SDYM as its classical equation of motion, its S
matrix is trivial. It is therefore NOT the theory of the N=2 string. We also
discuss the 5-dimensional actions that have been proposed for SDYM.
