A subject is to provide a nonaqueous electrolyte excellent in cycle performances such as capacity retention after cycling, output after cycling, discharge capacity after cycling, and cycle discharge capacity ratio, output characteristics, high-temperature storability, low-temperature discharge characteristics, heavy-current discharge characteristics, high-temperature storability, safety, high capacity, high output, high-current-density cycle performances, compatibility of these performances, etc. Another subject is to provide a nonaqueous-electrolyte secondary battery employing the nonaqueous electrolyte. The subjects have been accomplished with a nonaqueous electrolyte which contains a monofluorophosphate and/or a difluorophosphate and further contains a compound having a specific chemical structure or specific properties.