  We investigate equilibrium states, magnetic response and the normal
oscillations of internal degrees of freedom (Higgs modes and Goldstone modes)
of three-band superconductors accounting the terms of both internal proximity
effect and the ``drag'' effect (intergradient interaction) in the Lagrangian.
Both the Goldstone mode and the Higgs mode are split into three branches each:
common mode oscillations and two modes of anti-phase oscillations, which are
analogous to the Leggett mode in two-band superconductors. It is demonstrated
that the second and third branches are nonphysical, and they can be removed by
special choice of coefficients at the ``drag'' terms in Lagrangian. As a
result, three-band superconductors are characterized by only single coherence
length. Spectrum of the common mode Higgs oscillations has been obtained. The
magnetic penetration depth is determined with densities of superconducting
electrons in each band, although the drag terms renormalize the carrier masses.
