The tunneling into the bulk of a 2D electron system in a strong magnetic fi
eld is studied near integer quantum Hall transitions. We present a nonpertu
rbative calculation of the tunneling density of states (TDOS) for both Coul
omb and short-ranged electron-electron interactions. In the case of the Cou
lomb interaction, the TDOS exhibits a 2D quantum Coulomb gap behavior, v(ep
silon) = C-Q\epsilon\/e(4), where C-Q is a nonuniversal coefficient of quan
tum mechanical origin. For short-ranged interactions, we find that the TDOS
at low bias follows v(epsilon)/v(0) = 1 + (\epsilon\/epsilon(0))(gamma), w
here gamma is a universal exponent determined by the scaling dimension of s
hort-ranged interactions.