When considering multi-physics applications described by hyperbolic models, flow regimes, in comparison to single phase flows described by the Euler equations, are not characterized by one Mach number only. Examples are two fluid flows, where each phase is characterized by its own Mach number depending on the sound speed of the respective medium, or the simulation of elastic materials where, in addition to the standard acoustic Mach number, a shear Mach number depending on the shear modulus, describing the elastic shear stiffness of the material, can be defined. The characteristic speeds of these models scale with the inverse Mach number inflicting a very restrictive CFL condition on the time step for standard explicit schemes. Consequently, to avoid vanishing time steps, for near incompressible flows especially, implicit or implicit-explicit time integrators are necessary. Moreover, the monitoring of sound waves is usually less in the focus of a numerical simulation. Following the slower material waves and contact waves yields a less restrictive, Mach number independent CFL condition, which is advantageous when these slow dynamics are observed over a long time. In this talk we address implicit explicit time integration approaches for hyperbolic models involving the above mentioned applications as well as issues and difficulties arising in the construction of the corresponding finite volume scheme.