The a-type R-branch K-1=0 rotational transitions of the HCS and DCS radicals have been measured in the frequency range of 161 to 644 GHz using source modulation spectrometers. For DCS, the seven fine and hyperfine components of the 1(01)-0(00) rotational transition are also measured at 35 GHz using a Fourier transform millimeter-wave spectrometer. The spectra are found to be perturbed by the K-1=1 state through the off-diagonal spin-rotation interaction (epsilon(ab)+epsilon(ba))(NaSb+SbNa+NbSa+SaNb). In particular for DCS, strong perturbations are observed. The rotational constants, A, B+C, and B-C, of DCS are determined through an analysis of the perturbation. The r(0) structure of HCS has been determined as follows: r(0)(CH)=1.079(3) A, r(0)(CS)=1.562 28(3) A, and alpha(0)(HCS)=132.8(3)degrees. The quasilinearity parameter, gamma(0), is evaluated to be 0.80 for DCS, indicating that HCS is not a simple bent molecule.