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A "gleek" is the term that refers to a fan of Glee, the plural form being "gleeks." This term has been used several times in advertisements made by FOX, the most famous being the "Gleek Out!" group shot of the cast spilling slushies. The word "gleek" derives from the words "glee" and "geek" (glee + geek = gleek)
The 'k' is often seen in writing, next to the Glee heading, and usually there are slushies involved in the pictures.
Gleeks is the main label for those who are part of the Glee fanbase.
There is named a "Gleek" of the week after the episode has ended with the "gleek's" picture and name or username (Twitter).