The mechanisms of the ionization front advance in surface-wave-produced discharges are investigated using two experimental set-ups. The high-power surface waves are excited in a 3 cm wavelength band by a surfaguide and a novel type of launcher (an E-plane junction). The ionization front velocity of the surface wave is measured for a wide range of gas pressures, incident microwave power and initial pre-ionization. The experimental results are compared with theoretical ones based on three different models. The comparison between theory and experiment allows one to suggest a new interpretation of the ionization front's advance. The ionization front velocity is determined by a breakdown wave or an ionization wave in the electric field of a high-power surface wave in the zone near the ionization front.