Ni films of a few atomic layers are condensed in UHV at 10 K on metallic substrates of amorphous Pb75Bi25and crystalline Pb, Cu and Bi. Anomalous Hall effect measurements are used to determine the magnetization and the susceptibility of the films. Ni films with a thickness smaller than two atomic layers possess no magnetic moment but show an enhanced susceptibility. Between two and three atomic layers of Ni the susceptibility diverges and thicker films possess a magnetic moment. The experimental results can be well described with a band model of magnetism. A thin Ni film condensed onto a non‐magnetic metal represents a system in which the density of states is changed with thickness, causing a transition from Pauli paramagnetism to band ferromagnetism. In contrast to Ni the ferromagnetic metal Fe possess already for a coverage of 1/6 atomic layer a magnetic moment and shows a paramagnetic behavior.