Different magnetic states for a given real structure are known for bulk metals and alloys and also for free transition metal clusters. We have calculated the magnetic properties of small 3d transition metal clusters on the Cu(001) surface by means of an ab initio KKR Green's function method. It is shown that multiple magnetic states exist in these nanostructures. High spin and low spin ferromagnetic states as well as antiferromagnetic states occur. The energy differences between the different states are calculated.