  We consider quantum quenches in integrable models. We argue that the
behaviour of local observables at late times after the quench is given by their
expectation values with respect to a single representative Hamiltonian
eigenstate. This can be viewed as a generalization of the eigenstate
thermalization hypothesis to quantum integrable models. We present a method for
constructing this representative state by means of a generalized Thermodynamic
Bethe Ansatz (GTBA). Going further, we introduce a framework for calculating
the time dependence of local observables as they evolve towards their
stationary values. As an explicit example we consider quantum quenches in the
transverse-field Ising chain and show that previously derived results are
recovered efficiently within our framework.
