  Dynamical systems invariant under the action of the l-conformal Newton-Hooke
algebras are constructed by the method of nonlinear realizations. The relevant
first order Lagrangians together with the corresponding Hamiltonians are found.
The relation to the Galajinsky and Masterov [Phys. Lett. B 723 (2013) 190]
approach as well as the higher derivatives formulation is discussed. The
generalized Niederer's transformation are presented which relate the systems
under consideration to those invariant under the action of the l-conformal
Galilei algebra [Nucl. Phys. B 876 (2013) 309]. As a nice application of these
results an analogue of Niederer's transformation, on the Hamiltonian level, for
the Pais-Uhlenbeck oscillator is constructed.
