  We consider a description of membranes by (2,1)-dimensional field theory, or
alternatively a description of irrotational, isentropic fluid motion by a field
theory in any dimension. We show that these Galileo-invariant systems, as well
as others related to them, admit a peculiar diffeomorphism symmetry, where the
transformation rule for coordinates involves the fields. The symmetry algebra
coincides with that of the Poincare group in one higher dimension. Therefore,
these models provide a nonlinear representation for a dynamical Poincare group.
