We present accurate ab initio calculations of the NMR indirect spin-spin coupling constants of acetylene. Very large basis sets have been used in order to ensure near basis-set limit results for the different coupling constants, and large CI expansions enable an accurate treatment of electron correlation effects. The calculated coupling constants are in good agreement with recent experimental estimates of the coupling constants in an isolated acetylene molecule, corrected for rovibrational effects. The results demonstrate that experiment and theory finally have reached almost the same values for all the spin-spin coupling constants of the isolated, rigid acetylene molecule.