  We study collective amplitude modes of the superconducting order parameter in
strongly-coupled electron-phonon systems described by the Holstein model using
the nonequilibrium dynamical mean-field theory with the self-consistent Migdal
approximation as an impurity solver. The frequency of the Higgs amplitude mode
is found to coincide with the superconducting gap even in the strongly-coupled
(beyond BCS) regime. Besides the Higgs mode, we unravel another collective mode
involving the dynamics of both the phonons and the superconducting order
parameter. The frequency of this mode, higher than twice the renormalized
phonon frequency in the superconducting phase, is shown to reflect a strong
electron-mediated phonon-phonon interaction. Both types of collective
excitations contribute to time-resolved photoemission spectra after a strong
laser pump as vertex corrections to produce resonance peaks, which allows one
to distinguish them from quasiparticle excitations.
