Effects of electric field on electron emission rates have been studied for a number of deep level traps in electron-irradiated Ge crystals. Static electric fields have been induced by the application of a reverse bias to Au-Ge Schottky barriers. High-resolution Laplace deep level transient spectroscopy has been used to study electron emissions from double acceptor states of the vacancy-oxygen center and vacancy-group-V-impurity atom (Sb or Bi) pairs. It is found that in the range of moderate electric fields [(2-5)×104 V/cm] the electric-field enhancement of electron emission from the above traps can be described in the frame of a phonon-assisted tunneling model. This mechanism is characterized by the following dependence of electron emission rate on electric field E: e(E)/e(0)=exp(E2/Ech2), where Ech is characteristic field strength, which depends on tunneling time τ2. The values of Ech and τ2 have been determined and from the analysis of the values obtained conclusions on the adiabatic potential structures of the traps have been drawn. In the range of low electric fields (<2×104 V/cm) deviations from the phonon-assisted tunneling mechanism of the electric-field enhancement of electron emission have been observed for the traps studied. It appears that in this range of electric fields the e( E) dependencies can be described in the frame of the Poole-Frenkel mechanism rather than phonon-assisted tunneling.