Baumgartner B. Existence of many-particle bound states in spite of a pair-interaction with positive scattering length (24K, LATeX 2e) ABSTRACT. Examples of bound states are presented, for a system of three identical particles as well as for a system of particles on a lattice. The particles may be bosons as well as fermions. The interaction between them is given by a pair-potential, which does not allow two-particle bound states, has positive scattering length and is not too different from realistic interatomic potentials.