  The proximity effect in hybrid superconducting - normal metal structures is
shown to affect strongly the coherent oscillations of the superconducting order
parameter $\Delta$ known as the Higgs modes. The standard Higgs mode at the
frequency $2\Delta$ is damped exponentially by the quasiparticle leakage from
the primary superconductor. Two new Higgs modes with the frequencies depending
on both the primary and induced gaps in the hybrid structure are shown to
appear due to the coherent electron transfer between the superconductor and the
normal metal. Altogether these three modes determine the long-time asymptotic
behavior of the superconducting order parameter disturbed either by the
electromagnetic pulse or the quench of the system parameters and, thus, are of
crucial importance for the dynamical properties and restrictions on the
operating frequencies for superconducting devices based on the proximity effect
used, e.g., in quantum computing, in particular, with topological low-energy
excitations.
