A micromechanical system with a system that can vibrate, has a seismic mass and at least two spring elements. The spring elements are respectively fastened on one side externally to the seismic mass and on the other side to fixed anchor points of the micromechanical system such that the seismic mass can vibrate in a movement direction. In order to obtain a particularly large frequency spacing between the useful mode and further vibration modes of the system, at least one further spring element is provided in the inner region of the seismic mass. The further spring element the is fastened to a further anchor point of the micromechanical system. A method builds a micromechanical system with a system that can vibrate.