We experimentally demonstrate the first midinfrared (mid-IR) resonant magnetic nanostructures exhibiting a strong magnetic response corresponding to a negative permeability. This result is an important step toward the achievement of a negative refractive index in the IR. The possibility of extending negative permeability to higher frequencies is discussed; a structure with a negative effective permeability at a near-IR resonance frequency of 230 THz (1.3 microm) is proposed.