Strongly anisotropic electric-field enhancements of the thermal emission rates of electrons from the EL3 and EL5 deep-level defects in n-type GaAs crystal have been revealed with the double-correlation deep-level transient spectroscopy. The results, analysed by taking into account both the Poole–Frenkel and phonon-assisted tunnel effects, evidence a strong coupling of the defects to the lattice vibronic modes. The defect potential anisotropy of EL3 is consistent with the defect identification as an off-centre substitutional oxygen on the arsenic site. The revealed surprising break-down of the emission-rate enhancement, for the electric field applied along the ⟨1 0 0⟩ crystallographic direction, is interpreted as resulting from a possible reorientation of the EL3 defect, owing to a jump of the oxygen ion into a neighbouring lattice site, driven by a strong electric field. On the other hand, a close pair divacancy complex is suggested to be responsible for the EL5 defect.