Interface growth is a paradigmatic example of a complex system made from a large number of strongly interacting degress of freedom, with dynamical created long-range correlations. Such systems can undergo physical ageing, that is they display (i) slow relaxational behaviour, (ii) breaking of time-translation-invariance and (iii) dynamical scaling. Through simulations and simple exactly solvable models, we investigate into the existence of new, non-trivial dynamical symmetries extending dynamical scaling and their possible consequences.