A melt-spinning technique was used to produce metastable Zr-Ni and Hf-Ni alloys for compositions around the Ni-rich eutectic (at 89, 90, and 91 at. % Ni content). Depending on the cooling rate and alloy composition, either an amorphous (a) or a body-centered-cubic (bcc) phase or a nanocrystalline ͑n͒ state with the ͑Zr, Hf͒Ni 5 structure was formed. In this paper, experimental results on the low-temperature magnetic properties of these Zr-Ni and Hf-Ni ribbons are presented. The ac susceptibility, the low-field magnetization, and the magnetization isotherms were measured between 5 and 300 K. The Curie points of the amorphous and bcc phase of the Zr 9 Ni 91 alloy were practically the same (about 70 K) and the T C of the a-Zr 10 Ni 90 alloy was around 42 K, whereas the n-Hf 11 Ni 89 alloy remained Pauli paramagnetic down to 5 K. The results are evaluated in the framwork of the theory of very weak itinerant ferromagnetism. The critical concentration of Ni for the onset of ferromagnetism in these metastable alloys was deduced to be about 89.5 at. % Ni. The characteristics of the paramagnetic-ferromagnetic transition in these systems are discussed in terms of the electronic density of states at the Fermi level.