Abstract: Some fundamental problems on the establishment of the global unified height system, including the geometry and gravity definition of the normal height, the global unification of the regional height systems obtained from leveling measurements, and the determination of geoid potential W₀ are discussed. The main conclusions are summarized:①The definition of normal height in the sense of geometry leveling and gravity theory is different, so that h-ζ≠H^L, here h, ζ and H^L are geodetic height, height anomaly and levelling height respectively. Instead of it, we found H^L=h-ζ+∂γ/∂hζH, in the mountain area, the last correction term have to be added. ②Based on the merging of GNSS/gravity/regional leveling, the regional leveling height can be transformed into a global relative unified height system, however the value of geoid potential W₀ is still needed in order to establish an absolute height system. ③W₀ can be determinated from the modern geodetic techniques with a certain accuracy, but it is time variable, so that people may only define a global absolute unified height system in a fixed epoch.

Key words: height system, normal height, geoid potential