  We obtain a nonsmooth higher-order extension of Noether's symmetry theorem
for variational isoperimetric problems with delayed arguments. The result is
proved to be valid in the class of Lipschitz functions, as long as the delayed
higher-order Euler--Lagrange extremals are restricted to those that satisfy the
delayed higher-order DuBois--Reymond necessary optimality condition. The
important case of delayed isoperimetric optimal control problems is considered
as well.
