The microscopic origin of the static magneto-electric coupling, i.e. the change of magnetization with electric field or of polarization with magnetic field, is already well understood. Depending on the specific magnetic structure of the investigated materials, the exchange striction, the inverse Dzyaloshinskii-Moriya (D-M) interaction or the spin-dependent covalency between the metal d state and ligand p state may play the key role. In contrast, due to the dynamic magnetoelectric coupling, magnons can be excited in THz spectra by the electric component of the electromagnetic radiation; therefore, these excitations are called electromagnons and contribute to permittivity. Interestingly, different coupling mechanisms can be responsible for the static and dynamic magnetoelectric couplings in the same material. For example, in TbMnO3, the static polarization is induced along the crystallographic c axis by the inverse DM interaction due to a noncollinear spiral spin structure. Nevertheless, due to exchange striation, two broad electromagnons activate in the E||a polarized THz dielectric spectra. We investigated various materials with the Y- and Z-type hexaferrite structures. A small applied magnetic field induces a transverse conical ferrimagnetic structure where the inverse DM interaction is responsible for the appearance of a static polarization in the hexagonal plane. Electromagnons activate due to exchange striction in the E||c polarized THz spectra. Above 2-4 Tesla, the electromagnons and the static polarization disappear, because the magnetic structure transforms to a collinear one. During our talk we will also explain identical origin of static and dynamic magnetoelectric couplings in multiferroic Ni3TeO6.