The invention provides a soft magnetic thin strip which contains nanoscale fine grains and exhibits a high saturation magnetic flux density and excellent soft magnetic characteristics; a process for production of the same; magnetic parts; and an amorphous thin strip to be used in the production. In the invention, an amorphous thin strip is used, which is represented by the composition formula: Fe100-x-y-zAxMyXz-aPa (wherein A is at least one element selected from between Cu and Au; M is at least one element selected from among Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W and Mn; X is at least one element selected from between B and Si; and x, y, z and a (in terms of atomic percentage) satisfy the relationships: 0.5≦x≦1.5, 0≦y≦2.5, 10≦z≦23, and 0.35≦a≦10 respectively) and permits 180° bending. The amorphous thin strip can give through anneal a soft magnetic thin strip having a structure wherein grains of body-centered cubic structure having an average grain size of 60 nm or below are distributed in an amorphous phase with a grain volume fraction of 30% or above.