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 ChargeeXchange (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.