Heteroatom doping is a widely used method for the modification of the electronic and chemical properties of graphene. A low-pressure chemical vapor deposition technique (CVD) is used here to grow pure, nitrogen-doped and phosphorous-doped few-layer graphene films from methane, acetonitrile and methane-phosphine mixture, respectively. The electronic structure of the films transferred onto SiO2/Si wafers by wet etching of copper substrates is studied by X-ray photoelectron spectroscopy (XPS) and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy using a synchrotron radiation source. Annealing in an ultra-high vacuum at ca. 773 K allows for the removal of impurities formed on the surface of films during the synthesis and transfer procedure and changes the chemical state of nitrogen in nitrogen-doped graphene. Core level XPS spectra detect a low n-type doping of graphene film when nitrogen or phosphorous atoms are incorporated in the lattice. The electrical sheet resistance increases in the order: graphene < P-graphene < N-graphene. This tendency is related to the density of defects evaluated from the ratio of intensities of Raman peaks, valence band XPS and NEXAFS spectroscopy data.