  A quantum many-body system which is prepared in the ground state of an
integrable Hamiltonian does not directly thermalize after a sudden small
parameter quench away from integrability. Rather, it will be trapped in a
prethermalized state and can thermalize only at a later stage. We discuss
several examples for which this prethermalized state shares some properties
with the nonthermal steady state that emerges in the corresponding integrable
system. These examples support the notion that nonthermal steady states in
integrable systems may be viewed as prethermalized states that never decay
further. Furthermore we show that prethermalization plateaus are under certain
conditions correctly predicted by generalized Gibbs ensembles, which are the
appropriate extension of standard statistical mechanics in the presence of many
constants of motion. This establishes that the relaxation behaviors of
integrable and nearly integrable systems are continuously connected and
described by the same statistical theory.
