We present a space-time hierarchical solution concept for
optimization problems governed by the time-dependent Stokes-- and
Navier--Stokes system.
Discretisation is carried out with finite elements in space and
one-step-$/theta$-schemes in time.
By combining a Newton solver for the treatment of the nonlinearity
with a space-time multigrid solver for linear subproblems, we
obtain a robust solver whose convergence behaviour is independent of
the number of unknowns of the discrete problem and robust with regard to
the considered flow configuration.