The magnetic properties and stability of hydrogenated, amorphous, compositionally modulated (CM) Fe-Zr thin films were studied in this work. These films had average compositions FexZr100-x with x=80, 82, 85 modulation periods of similar to 10 Angstrom, and total thicknesses of similar to 1000 Angstrom. In comparison with results obtained for similar homogeneous films, the CM films could be electrochemically charged with larger amounts of hydrogen in much shorter times. The hydrogen induced increases (HIC) in the Curie temperatures of CM films were comparable to those reported for homogeneous films, but the increases in the magnetizations were greater. While the HIC in the magnetizations were greater. While the HIC in the magnetic state of homogeneous films are reversed by hydrogen effusion, in CM films they relax to a stable, irreversible, soft magnetic state with interesting magnetic properties.