Nightmare Spectres are dark cyan tinted faster and more powerful forms of spectres found in the PlayStation version of Doom. They appear in the Sega Saturn version as well, but with the same sprites as the port's respective spectres, only larger.
They were also added to the Doom 64 TC (they were not in the original game) where they have their own sprite.
The manual of the PSX version says: If you "Liked" the spectre meet his tougher brother.
The manual of the Sega Saturn version says: If you "Liked" the spectre and you'll love this big bad brother.