The major sources of the Soft X-ray Background (SXRB), besides distinct structures as supernovae and superbubbles (e.g. Loop I), are: (i) an absorbed extragalactic emission following a power law, (ii) an absorbed thermal component (∼2×10 6 K) from the galactic disk and halo, (iii) an unabsorbed thermal component, supposedly at 10 6 K, attributed to the Local Bubble and (iv) the very recently identified unabsorbed Solar Wind Charge-eXchange (SWCX) emission from the heliosphere and the geocorona. We study the SWCX heliospheric component and its contribution to observed data. In a first part, we apply a SWCX heliospheric simulation to model the oxygen lines (3/4 keV) local intensities during shadowing observations of the MBM 12 molecular cloud and a dense filament in the south galactic hemisphere with Chandra, XMM-Newton, and Suzaku telescopes. In a second part, we present a preliminary comparison of SWCX model results with ROSAT and Wisconsin surveys data in the 1/4 keV band. We conclude that, in the 3/4 keV band, the total local intensity is entirely heliospheric, while in the 1/4 keV band, the heliospheric component seems to contribute significantly to the local SXRB intensity and has potentially a strong influence on the interpretation of the ROSAT and Wisconsin surveys data in terms of Local Bubble hot gas temperature.