Electron tunnel transport across single-barrier GaAs/AlAs/GaAs heterostructures is investigated. It is shown that “zero bias anomalies”—extrema in differential conductivity close to the zero bias—in the structures investigated are caused by resonance tunneling between parallel two-dimensional electron gases in enriched layers, which are formed from both sides of the barriers due to the presence of Si donor impurities in barriers. The suppression of resonance tunneling between parallel two-dimensional electron gases is found in narrow ranges close to the zero bias (tunnel gap) in a strong magnetic field parallel to the current direction only when a single Landau level is occupied for each of the two-dimensional electron gases. Suppression is induced by a Coulomb gap at the Fermi level in the tunnel density of states. This experiment originally revealed the manifestation of a Coulomb gap in tunneling between parallel two-dimensional electron gases with relatively low mobilities. For these electron gases, the influence of disorder or random potential fluctuations on the mechanism of formation of the tunnel gap is noticeable.