  We give the algebra of quasimodular forms a collection of Rankin-Cohen
operators. These operators extend those defined by Cohen on modular forms and,
as for modular forms, the first of them provide a Lie structure on quasimodular
forms. They also satisfy a ``Leibniz rule'' for the usual derivation.
Rankin-Cohen operators are useful for proving arithmetic identities. In
particular we give an interpretation of the Chazy equation and explain why such
an equation has to exist.
