  Let $f\in \mathbb{C}[X_1,..., X_n]$ be a homogeneous polynomial and B(f) be
the corresponding Brieskorn module. We describe the torsion of the Brieskorn
module B(f) for n=2 and show that any torsion element has order 1. For n>2, we
find some examples in which the torsion order is strictly greater than 1.
