The magnetization processes of the Y(Co1-xNix)(5) system were measured at 4.2 K in pulsed high magnetic fields up to 40 T. The spontaneous magnetization decreases linearly with increasing Ni concentration up to x = 0.4. In the narrow concentration region 0.5less than or equal toxless than or equal to0.6, the magnetization rapidly decreases, but weak ferromagnetism persists up to x = 0.8. On the other hand, the high-field susceptibility exhibits a maximum at x = 0.55. These results show that the magnetic state of Y(Co1-xNix)(5) changes from the high- to the low-moment state at the critical concentration x = 0.55. In the vicinity of this concentration, the magnetization was measured at high pressures up to 1 GPa. The compound Y(CO0.5Ni0.5)(5) shows a very large pressure effect, indicating that it is very close to the critical concentration. (C) 2003 Elsevier Science B.V. All rights reserved.