  We use series expansions to study the excitation spectra of spin-1/2
antiferromagnets on anisotropic triangular lattices. For the isotropic
triangular lattice model (TLM) the high-energy spectra show several anomalous
features that differ strongly from linear spin-wave theory (LSWT). Even in the
Neel phase, the deviations from LSWT increase sharply with frustration, leading
to roton-like minima at special wavevectors. We argue that these results can be
interpreted naturally in a spinon language, and provide an explanation for the
previously observed anomalous finite-temperature properties of the TLM. In the
coupled-chains limit, quantum renormalizations strongly enhance the
one-dimensionality of the spectra, in agreement with experiments on Cs_2CuCl_4.
