We studied the transition from the electrochemical double-layer charging regime to intercalative doping of bundled single-walled carbon nanotubes (SWNT) in KCl and HCl aqueous solution. For this purpose we used high doping levels by applying constant potentials above 1000 mV approaching and slightly exceeding the oxidation potential for Cl(-) ions. At each potential in situ Raman measurements of the radial breathing mode (RBM), the high-energy tangential mode (HEM), and the disorder-induced (D) mode were performed. Furthermore, the conductivity and reflectivity of a set of SWNT samples were measured as a function of doping and subsequently the samples were examined by X-ray photoelectron spectroscopy (XPS). From a comparative analysis of the results we conclude that above 1000 mV a significant penetration of chlorine species into the interstitial channels of the SWNT bundles and possible covalent functionalization take place.