Abstract: I will introduce a new class of groups - finitely determined groups of local similarities on a compact ultrametric space - and prove that they have the Haagerup property (that is, they are a-T-menable in the sense of Gromov). The class includes Thompson's groups, which have already been shown to have the Haagerup property by Dan Farley, as well as many other groups acting on boundaries of trees. The Haagerup property for a group means that there is a proper, affine isometric action of the group on some Hilbert space. Higson and Kasparov proved that such groups satisfy the Connes-Baum conjecture.