We prove the strong normalisation for any PTS, provided the existence of a certain $\Lambda$-set $\A for every sort s of the system. The properties verified by the $\A's depend of the axioms and rules of the type system. A slightly shortened version of this work has been published under the same title in the volume «Types for Proofs and Programs», Internatio- nal workshop TYPES'96, E. Gimenez and C. Paulin-Mohring Eds, LNCS 1512, Springer-Verlag, 1998.