  We construct the systems of the harmonic and Pais-Uhlenbeck oscillators,
which are invariant with respect to arbitrary noncompact Lie algebras. The
equations of motion of these systems can be obtained with the help of the
formalism of nonlinear realizations. We prove that it is always possible to
choose time and the fields within this formalism in such a way that the
equations of motion become linear and, therefore, reduce to ones of ordinary
harmonic and Pais-Uhlenbeck oscillators. The first-order actions, that produce
these equations, can also be provided. As particular examples of this
construction, we discuss the $so(2,3)$ and $G_{2(2)}$ algebras.
