Dual Definitional model
This model of asexuality was developed by mandrewliter, although he has since come to question it. It says that in asexual discourse, the word ‘asexual’ really has two related, but conceptually distinct, meanings. The first is a sexual orientation. An asexual is a person who experiences little or no sexual attraction. The second definition is an identity based on that sexual orientation: An asexual is someone who experiences little or no sexual attraction and calls themself asexual. This identity is based on not only experiencing little or no sexual attraction, but on the effects of that within the cultural contexts in which people live.
This model uses the phrase “a person who experiences little or no sexual attraction” because the boundary between sexual and asexual is blurry and there is no clear line to draw between them. The question of where to draw the line is something each person decides for themself, so self-identification answers the question of who is and who isn’t asexual. A longer explanation is given on his blog