It is hardly determined some details of the local atomic structures in multi-component non-crystalline systems by the ordinary x-ray diffraction method. I have applied the anomalous x-ray scattering (AXS) method to overcome these difficulties in the non-crystalline systems containing more than two elements. In the present paper, I will present my recent studies of the local atomic structures in a new type of amorphous alloys with an extremely wide super-cooled liquid region and of metallic complexes in Ni-Mo electroplating aqueous solutions. The usefulness of the AXS method in the studies of the non-crystalline materials will be demonstrated.