Uniform S = 1 and 1/2 Heisenberg antiferromagnetic chains have a quantum singlet ground state which is an eigenstate of the total spin with S(tot) = 0. However, the 'internal' order of these ground states is quite different, and is reflected in gapless excitations in the S = 1/2 state, while the S = 1 chain has a triplet excitation gap known as the Haldane gap. The exchange interactions of the antiferromagnets CsNiCl(3) (S = 1) and Cu-tetraminsulfate (S = 1/2) are quasi-one dimensional, leading to long-range ordered Neel ground states. Nevertheless, we find evidence of quantum spin dynamics. (C) 2000 Elsevier Science B.V. All rights reserved.