In this thesis the differential invariant cross sections of the inclusive pi0 and eta meson production in proton-proton collisions at sqrt(s) = 0.9, 2.76 and 7TeV are presented. They have been obtained by the reconstruction of electrons and positrons from photon conversions in the Inner Tracking System and the Time Projection Chamber of the ALICE experiment. Therefore, the method is completely independent of calorimeters and allows the extraction of the pi0 (eta) signal down to very low transverse momenta of 0.3 GeV/c (0.4 GeV/c) for sqrt(s) = 7TeV. The resulting differential invariant cross sections are compared to those of the PHOton Spectrometer and charged pions and found to be almost everywhere in good agreement. The combined spectra of the photon conversion method and PHOS cover a broad transverse momentum range. The pi0 and eta spectra agree with NLO perturbative QCD predictions at sqrt(s) = 0.9TeV, however, the calculations overestimate the data at sqrt(s) = 7TeV. Also mT scaling has been tested at sqrt(s) = 2.76 and 7TeV. For sqrt(s) = 2.76TeV no clear statement can be made while for sqrt(s) = 7TeV an indication of violation is observed at low mT . The measured eta/pi0 ratios at the different energies are in agreement with world data. Furthermore, the production of pi0 mesons as a function of charged particle multiplicity has been investigated for sqrt(s) = 7TeV. A strong dependence is observed. With increasing charged-particle multiplicity an increase of the neutral pion yield and of the average transverse momentum is seen