This article discusses the relationship between the inertial manifolds "with
delay" introduced by Debussche & Temam, and the standard definition. In particular, the
"multi-valued" manifold of the same paper is shown to arise naturally from the manifolds
"with delay" when considering issues of convergence as the delay time tends to infinity.
This leads to a new characterisation of the multi-valued manifold, which allows a fuller
understanding of its structure.