  Prethermalization has been extensively studied in systems close to
integrability. We propose a more general, yet conceptually simpler, setup for
this phenomenon. We consider a---possibly nonintegrable---reference dynamics,
weakly perturbed so that the perturbation breaks at least one conservation law
of the reference dynamics. We argue then that the evolution of the system
proceeds via intermediate (generalized) equilibrium states of the reference
dynamics. The motion on the manifold of equilibrium states is governed by an
autonomous equation, flowing towards global equilibrium in a time of order
1/g^2, where g is the perturbation strength. We also describe the leading
correction to the time-dependent reference equilibrium state, which is, in
general, of order g. The theory is well confirmed in numerical calculations of
model Hamiltonians, for which we use a numerical linked cluster expansion and
full exact diagonalization.
