  Two hyperbolic-deformed field theoretic models are discussed. In both of
them, due to the effect of specific deformation function on the well known
$\varphi^4$ and $\varphi^6$ models, their internal structure may change
significantly. Unlike the $\varphi^4$ kinks solutions, which has only one
internal mode in addition to its translational mode, the kinks of the
hyperbolic-deformed $\varphi^4$ model can have several internal modes.
Moreover, the deformation on the $\varphi^6$ model has other interesting
features, because the kinks of the $\varphi^6$ model have only a zero mode and
the deformation may cause the appearance of internal mode for both kink and
antikink. The presence of the new internal modes modify the collisions which we
explore in the present work. The deformation relies on a real parameter, which
controls the number of internal modes, and we also study how the deformation
parameter alter the mass of the kinks and the critical velocities involved in
the collisions.
