  We consider time evolution in models close to integrable points with hidden
symmetries that generate infinitely many local conservation laws that do not
commute with one another. The system is expected to (locally) relax to a
thermal ensemble if integrability is broken, or to a so-called generalised
Gibbs ensemble if unbroken. In some circumstances expectation values exhibit
quasi-stationary behaviour long before their typical relaxation time. For
integrability-breaking perturbations, these are also called pre-thermalisation
plateaux, and emerge e.g. in the strong coupling limit of the Bose-Hubbard
model. As a result of the hidden symmetries, quasi-stationarity appears also in
integrable models, for example in the Ising limit of the XXZ model. We
investigate a weak coupling limit, identify a time window in which the effects
of the perturbations become significant and solve the time evolution through a
mean-field mapping. As an explicit example we study the XYZ spin-$\frac{1}{2}$
chain with additional perturbations that break integrability. One of the most
intriguing results of the analysis is the appearance of persistent oscillatory
behaviour. To unravel its origin, we study in detail a toy model: the
transverse-field Ising chain with an additional nonlocal interaction
proportional to the square of the transverse spin per unit length [Phys. Rev.
Lett. 111, 197203 (2013)]. Despite being nonlocal, this belongs to a class of
models that emerge as intermediate steps of the mean-field mapping and shares
many dynamical properties with the weakly interacting models under
consideration.
