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Dynamical spin correlation functions in (q, ω)-space are calculated numerically for linear quantum-mechanical Heisenberg systems containing up to ten spins with s = 1/2 and s = 1. We consider ferro- and antiferromagnets including single-site and exchange anisotropies. We compare our results with various other theoretical treatments and draw conclusions for the dynamics of infinite chains. In the case of the s = 1 planar Heisenberg ferromagnet direct comparison is made with inelastic neutron scattering cross sections of CsNiF3. The theoretical and experimental results are in good agreement.