  The paper introduces a technique that decomposes the dynamics of a nonlinear
system about an equilibrium into low order components, which then can be used
to reconstruct the full dynamics. This is a nonlinear analogue of linear modal
analysis. The dynamics is decomposed using Invariant Spectral Foliations (ISF),
which is defined as the smoothest invariant foliation about an equilibrium and
hence unique under general conditions. The conjugate dynamics of an ISF can be
used as a reduced order model. An ISF can be fitted to vibration data without
carrying out a model identification first. The theory is illustrated on a
analytic example and on free-vibration data of a clamped-clamped beam
