An ILH manifold – for a (possibly infinite dimensional) manifold modelled on an inverse limit of Hilbert spaces – is a topological manifold equipped with a kind of smooth structure that is more general than that of a Hilbert manifold but less general than that of a Fréchet manifold.
H. Omori, Infinite dimensional Lie transformation groups, Springer lecture notes in mathematics 427 (1974)
H. Omori, Infinite dimensional Lie groups, translations of Mathematical monographs, 158