Of Monsters and Men are best known for a lighter folk-pop sound, but "Alligator" finds the Icelandic band utilizing a heavier kick than usual.
The driving, percussion-heavy track was penned by co-vocalist Nanna Bryndis Hilmarsdóttir. She recalled to NME
that it came very deep into the writing process for the Fever Dream
album. Usually she'd write on an acoustic guitar and guitarist Raggi Þórhallsson would "flesh it out in a very singer-songwriter kind of way." However she'd become tired of this method of writing and was looking for ways to challenge herself. For this song, she did a lot more writing on the computer and explored sounds there.