In his early works, Schrödinger investigated links between 
quantum dynamics and so called classical dynamics (given by Newton's equation). To do this, he introduced "coherent states", functions that are as concentrated in position and momentum as a wave function can get, hence often used to describe the equivalent of a point. He said that the quantum evolution of such states should be well approximated by a coherent state propagated using only classical dynamics. The proper setting to make such approximation is semiclassical analysis, regime where $h$ can be treated as a very small constant. Following this idea, the goal of this talk is to obtain a handy description of coherent states propagated up to times close to the Ehrenfest one, under the hypothesis of normal hyperbolicity of the classical dynamics.