  In this paper, we give two elementary constructions of homogeneous
quasi-morphisms defined on the group of Hamiltonian diffeomorphisms of certain
closed connected symplectic manifolds (or on its universal cover). The first
quasi-morphism, denoted by $\calabi\_{S}$, is defined on the group of
Hamiltonian diffeomorphisms of a closed oriented surface $S$ of genus greater
than 1. This construction is motivated by a question of M. Entov and L.
Polterovich. If $U\subset S$ is a disk or an annulus, the restriction of
$\calabi\_{S}$ to the subgroup of diffeomorphisms which are the time one map of
a Hamiltonian isotopy in $U$ equals Calabi's homomorphism. The second
quasi-morphism is defined on the universal cover of the group of Hamiltonian
diffeomorphisms of a symplectic manifold for which the cohomology class of the
symplectic form is a multiple of the first Chern class.
