Let F be a quadratic extension of the field of p-adic numbers and k an algebraic closed field of characteristic p. We say that a smooth representation of GL2(F) on a k-vector space is of finite presentation if it is a of finite presentation in the category of smooth representations of GL2(F). In this talk we prove that if F is different of Qp, irreducible supersingular representations of GL2(F) on k-vector spaces are not of finite presentation.