  We study the quantum cohomology of quasi-minuscule and quasi-cominuscule
homogeneous spaces. The product of any two Schubert cells does not involve
powers of the quantum parameter higher than 2. With the help of the quantum to
classical principle we give presentations of the quantum cohomology algebras.
These algebras are semi-simple for adjoint non coadjoint varieties and some
properties of the induced strange duality are shown.
