**Abstract:**

The lambda-calculus with multiplicities is a refinement of the lazy
lambda-calculus where the argument in an application comes with a
multiplicity, which is an upper bound to the number of its uses. This
introduces potential deadlocks in the evaluation. We study various
observation scenarios for this calculus, depending on the way we
observe termination, deadlock and divergence. We relate these
observational semantics with the intensional interpretation of
lambda-terms, by means of Lévy-Longo trees. We show in particular
that the inclusion of such trees coincides with the ``flat''
observational semantics, where deadlocks and convergence are
distinguished.