A detailed study of the slow manifold of a model exhibiting mixed-mode oscillations is presented. A scenario for the emergence of mixed-mode states which does not involve phase locking on a 2-torus is constructed. We show that mixed-modes correspond to the periodic orbits embedded in the horseshoe-type strange set and demonstrate how transformations of this set determine the transitions of mixed-mode states into each other. (C) 1997 American Institute of Physics.