Face-centered cubic Pd–Cr alloys with 25%–35% Cr, quenched from 1200°C, have an average paramagnetic moment μ̄Cr of 0.5–1.2 μB. Below Tf=36°–76°K the moments are largely frozen, without long-range magnetic order, but ferromagnetic clusters of up to about 24 μB account for the thermomagnetic or isothermal remanence. These giant moments can be aligned in successive small thermally activated steps by cooling in a magnetic field. Once aligned, the giant moments can be turned collectively by much smaller fields. The bcc V–Mn alloys with 50%–76% Mn have similar magnetic properties, but with supergiant moments of more than 1000 μB, as quenched from 1200°C. For the Pd alloys with more than 25% Cr the minimum fields and temperatures necessary to align the moments are decreased considerably by annealing at 400°C, when the ferromagnetic clusters acquire dipole moments of up to 3600 μB, as measured in the superparamagnetic state, above Tf. The total moment of all supergiant clusters in the annealed 33% Cr alloy is equal to the thermomagnetic remanence of this alloy at 4.2°K. In the quenched as well as in the annealed condition the alloys with 29% and 33% Cr show the largest thermomagnetic remanence, presumably because the tendency for atomic ordering is largest at these compositions.