Energetic neutral atoms (ENA's) which are produced in the heliospheric interface can be used to remotely investigate this highly interesting, but poorly known region acting as buffer against the interstellar plasma. To optimally take advantage from this very promising observational technique, based on ENA flux measurements, one needs to know the spectral production rate of the ENA's in the heliosheath and about the foreground ENA contaminations originating in the inner heliosphere, e.g. inside the termination shock. Heliosheath ENA's with energies of about a few KeV originate from charge exchange reactions of H-atoms both with the shocked solar wind protons and with pick-up protons downstream of the termination shock. Inner heliospheric ENA's detectable at the Earth can only originate from H charge exchange reactions with pick-up protons. In this article we calculate on the basis of the five-fluid Bonn model the time-dependent ENA fluxes that are connected with these three sources and compare them. It will be demonstrated that the heliosheath ENA fluxes dominate from nearly all directions over the inner heliospheric ENA fluxes, though the best chances to disentangle the contributions appear in upwind and downwind direction at specific periods of the solar activity cycle.