We investigate the formation of a spin gap in one-dimensional models characterized by groups with hidden dynamical symmetries. A family of two-parametric models of isotropic and anisotropic spin-rotator chains (SRC's) characterized by SU(2)×SU(2) and SO(2)×SO(2)×Z ₂×Z ₂ symmetries is introduced to describe the transition from SU(2) to SO(4) antiferromagnetic Heisenberg chains. The excitation spectrum is studied with the use of the Jordan-Wigner transformation generalized for o ₄ algebra and by means of the bosonization approach. Hidden discrete symmetries associated with invariance under various particle-hole transformations are discussed. We show that the spin gap in SRC Hamiltonians is characterized by the scaling dimension 2/3, in contrast to dimension 1 in the conventional Haldane problem.