  From the underlying non-linear realisation we compute the complete E11
invariant equations of motion in eleven dimensions, at the linearised level, up
to and including level four in the fields. Thus we include the metric, the
three and six forms, the dual graviton and three fields at level four. The
fields are linked by a set of duality equations, which are first order in
derivatives and transform into each other under the E11 symmetries. From these
duality relations we deduce second order equations of motion, including those
for the usual supergravity fields. As a result the on-shell degrees of freedom
are those of the eleven dimensional supergravity. We also show that the level
four fields provide an eleven dimensional origin of Romans theory and lead to a
novel duality relation.
