[en] The CAST (CERN Solar Axion Telescope) experiment is searching for solar axions by their conversion into photons inside a transverse magnetic field. So far, no solar axionsignal has been detected, but a new upper limit could be given (CAST Phase I). Since 2005, CAST entered in its second phase where it operates with a buffer gas (⁴He) in the conversion region to extend the sensitivity of the experiment to higher axionmasses. For the first time it is possible to enter the theoretically favored axion massrange and to give an upper limit for this solar axion mass-range (>0.02 eV). This thesis is about the analysis of the X-ray telescope data Phase II with ⁴He inside the magnet. The result for the coupling constant of axions to photons is: g_αγγ<1.6-6.0 x 10^-10 GeV^-1 (95%C.L.) for m_a=0.02-0.4 eV. (2) This result is better than any result that has been given before in this mass range for solar axions. (orig.)