These are
demons in
Kia Asamiya's
Silent Mobius manga and
anime series. They reside in another dimension, in a world called
Nemisis. Also called entities, they were brought into the human dimension by the mage Gilgelf Liqueur, the father of
Katsumi Liqueur. They are the sworn enemies of the
AMP and stop at nothing to kill them.
They work with a group of humans led by a man called Maximillian Ganossa. While lower-powered Lucifer Hawks merely attack humans to feed, the more intelligent and powerful ones have a different objective, seeking to bring Katsumi Liqueur to Nemisis, as this will open the gateway between their world and Earth. In some cases, Lucifer Hawks try to absorb the powers of some AMP members by taking their bodies into their own. However in both cases they are stopped by the rest of the team.
Originally relations between Earth and Nemisis were cordial. Some Lucifer Hawks had produced children by humans (though little detail is provided on whether men, as well as women, had Lucifer Hawk spouses). However after some years the gateway between the two dimensions had caused too much opposite energy to flow into each world. In order to restore the correct balance, Project Gaia was conceived, which would then seal the barrier forever. However it was sabotaged by Ganossa, who had his own agenda - the gateway stayed open and ravaged Earth (and possibly Nemisis too). No one realises this, so the Lucifer Hawks wrongly blame Gilgelf and the humans.