The present invention provides an additive which is able to make a non-aqueous-electrolyte secondary cell or a non-aqueous electrolyte electric double layer capacitor which is excellent in low-temperature characteristics, while maintaining a necessary cell properties, and a non-aqueous-electrolyte secondary cell or a non-aqueous electrolyte electric double layer capacitor that contains therein the additive. The additive contains at least one of tautomers of phosphazene derivatives represented by formulae (1) and (2): ##STR00001## wherein R.sup.1, R.sup.2 and R.sup.3 independently represent a monovalent substituent or a halogen element; X represents a substituent containing at least one selected from a group of carbon, silicon, germanium, tin, nitrogen, phosphorus, arsenic, antimony, bismuth, oxygen, sulfur, selenium, tellurium and polonium; and Y.sup.1 and Y.sup.2 independently represent a divalent connecting group, a divalent element or a single bond.