The pressure effect on crystal structures, lattice vibrations, and electrical transport properties of PdS2 and NiSe2 were studied under high pressures of up to ~50 GPa using Raman spectroscopy and electrical resistivity measurements. PdS2 undergoes semiconductor-to-metal transition at a pressure of ~7 GPa without a structural phase transition. Structural transition to the pyrite-type phase occurs at a pressure of ~16 GPa. Superconductivity emerges in the pyrite-type phase of PdS2 with a well-defined dome-shaped dependence of critical temperature of superconductivity on pressure, with a maximum value of 8.0 K at 37.4 GPa. Although this behavior is similar to that in isostructural PdSe2, correlation with anomalous anion bond softening at critical temperature is not observed in PdS2 in contrast to PdSe2. Conversely, the anion bond instability is observed by the softening of the Se22− internal vibrational Raman mode in pyrite NiSe2 under pressure. Despite the persisting structural instability due to destabilization of Se22− dimers, NiSe2 remains a normal nonsuperconducting metal.