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We prove the stability of de Sitter space-time as a solution to theEinstein-Vlasov system with massless particles. The semi-global stability ofMinkowski space-time is also addressed. The proof relies on conformaltechniques, namely Friedrich's conformal Einstein field equations. We exploitthe conformal invariance of the massless Vlasov equation on the cotangentbundle and adapt Kato's local existence theorem for symmetric hyperbolicsystems to prove a long enough time of existence for solutions of the evolutionsystem implied by the Vlasov equation and the conformal Einstein fieldequations.

The Conformal Einstein Field Equations with Massless Vlasov Matter