  We examine whether the Painlev\'e property is a necessary condition for the
integrability of nonlinear ordinary differential equations. We show that for a
large class of linearisable systems this is not the case. In the discrete
domain, we investigate whether the singularity confinement property is
satisfied for the discrete analogues of the non-Painlev\'e continuous
linearisable systems. We find that while these discrete systems are themselves
linearisable, they possess nonconfined singularities.
