Magnetic properties of amorphous Fe38Ni38B12P5Si3Nb3Cu1 alloy ribbons have been investigated in as-spun and annealed states with the aim of developing an ultrasoft magnetic material which is expected to be used in advanced information data devices. A small amount of simultaneous addition of Cu and Nb to a FeNi-metalloid amorphous alloy system caused the change in crystallization process from eutectic type to the primary one. After annealing at the temperature just below the glass transition temperature (Tg), the glassy alloy ribbon exhibit excellent soft magnetic properties, very low coercive force of 1 A/m and extremely high effective permeability of 7.5·104 at 1 kHz which have not been obtained for any kinds of Fe- and Ni-based amorphous alloys, in spite of relatively low saturation magnetic flux density of 0.86 T. The further increase in annealing temperature causes the precipitation of nanoscale fcc particles with a size of about 7 nm including a high density of planar faults and the resulting nanostructure alloy also exhibits good soft magnetic properties with low Hc below 2 A/m. The formation of nanostructure fcc-(Fe,Ni) + glass soft magnetic alloys is also novel. The syntheses of the new Fe-Ni-based glassy and nanocrystalline [fcc(Fe,Ni) + glass] alloy ribbons with ultrasoft magnetic properties are encouraging as a new type of energy saving-type soft magnetic material.