**Abstract:**
(see also RR-2441)

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 the
discriminating power of this calculus over the usual lambda-terms. We
prove in particular that the observational equivalence induced by
contexts with multiplicities coincides with the equality of
Lévy-Longo trees associated with lambda-terms. This is a
consequence of the characterization we give of the corresponding
observational precongruence, as an extensional preorder involving
eta-expansion, namely Ong's lazy Plotkin-Scott-Engeler
preorder.