Experimentally and theoretically (ab initio) determined CC spin-spin coupling tensors and H-1 and C-13 nuclear shielding tensors are reported for ethane ((C2H6)-C-13), ethene ((C2H4)-C-13), and ethyne ((C2H2)-C-13). The experimental anisotropies of the CC coupling tensors, Delta J(CC), for all these molecules, and also the combination J(CC,xx)-J(CC,yy) for ethene, were derived from sets of anisotropic couplings (D-exp) analyzed from the H-1 and C-13 NMR spectra of molecules partially oriented in liquid-crystalline environments. Both harmonic vibrations and structural deformations arising from the correlation of vibrational and reorientational motions were taken into account in the D couplings. The ab initio calculations of all the J tensors were performed using MCSCF linear response theory. The best calculated and experimental Delta J(CC) values (along with J(CC,xx)-J(CC,yy) for ethene) an found to be in good mutual agreement. Together with earlier work on the (n)J(CC) tensors in benzene, this study shows that the indirect contribution, 1/2J(CC)(aniso), to experimental couplings between differently hybridized carbons is small and can generally be omitted. This means that the use of experimental D-CC couplings in the determination of molecular order tensors and/or conformation does not introduce serious errors. The experimental determination of the H-1 and C-13 Shielding tensors was based on the liquid crystal director rotation by 90 degrees in mixtures of thermotropic nematogens with opposite anisotropy of diamagnetic susceptibility. Ab initio SCF and MCSCF calculations utilizing gauge-including atomic orbitals produce results in good agreement with experiments.