The mode structure of global drift waves in tokamaks, which are not lo
calized by magnetic shear and density inhomogeneity, is investigated i
n the framework of fully two-dimensional problems. We obtain the analy
tically explicit, two dimensional expressions for the electrostatic po
tential of global drift waves, distinguishing between the weak and str
ong regimes with respect to the strength of torodicity (the ratio of t
he density scale length to the major radius). The former is found to h
ave an up-down asymmetry of the phase function on the cross-section of
the torus, while the latter has that of both the phase function and t
he amplitude.