  We construct the non-linear realisation of the semi-direct product of E11 and
its vector representation in five and eleven dimensions and find the dynamical
equations it predicts at low levels. Restricting these results to contain only
the usual fields of supergravity and the generalised space-time to be the usual
space-time we find the equations of motion of the five and eleven dimensional
maximal supergravity theories. Since this non-linear realisation contains
effects that are beyond the supergravity approximation and are thought to be
present in an underlying theory we conclude that the low energy effective
action of string and branes must possess an E11 symmetry.
