Abstract In cubic and near-cubic ionic and semiconducting compounds, we can find two correlationships among the optical dielectric constant ϵ∞, short-range and long-range forces. In the relationships, the chemical valence of high ionic conductors takes the value shifted from the formal value. The shift can be explained from the effect of d-electron energy level near the band gap. A linear relationship of ln (ϵ∞) to ln ( T c ) is found for fast-ionic conductors. From these relations, intimate correlation of the band gap energy to the fast-ionic conduction is suggested.