  In this article we prove the irreducibility of the Hilbert scheme of
rationnal curves on homogeneous varieties with fixed class in the Chow ring.
This result has also been proved by J. F. Thomsen [T] and B. Kim and R.
Pandharipande [KP]. Our method is totaly different (we don't use the
compactification of stable maps) and enables us to prove the existence of
rational smooth curves on homogeneous varities with fixed class in the Chow
ring. This was not the case of Thomsen's and Kim and Pandharipande's proofs. We
use a decomposition of G/P in orbits (called the P'-orbits, see definition)
which are bigger than the Schubert cells. We then prove that these P'-orbits
are "towers" of affine bundles (see definition) over "smaller" homogeneous
varities. This description gives the results. Our decomposition in P'-orbits
enables us to give a "better" desingularisation of Schubert varities than
Demazure's one.
