Ab initio equation of motion coupled cluster singles and doubles (EOM-CCSD) and second-order polarization propagator approximation (SOPPA) calculations have been performed to evaluate spin-spin coupling constants for FCCF (difluoroethyne). The computed EOM-CCSD value of 3 J(F-F) obtained at the experimental geometry of this molecule supports the previously reported experimental value of 2.1 Hz, thereby resolving an apparent discrepancy between theory and experiment. This coupling constant exhibits a strong dependence on the C-C and C-F distances, and its small positive value results from a sensitive balance of paramagnetic spin-orbit (PSO) and spin-dipole (SD) terms. The three other unique FCCF coupling constants 1 J(C-C), 1 J(C-F), and 2 J(C-F) have also been reported and compared with experimental data. While 1 J(C-F) is in agreement with experiment, the computed value of 2 J(C-F) is larger than our estimate of the experimental coupling constant. Copyright