Hall effect, electron mobility, and electric conductivity in n‐ZnSe crystals doped with acceptor copper impurity are studied in the temperature range 77 to 300 K. The increase of copper content in samples results in a drastic increase in the conductivity of crystals, in a decrease in electron concentration, and in abnormally low mobility values. When the samples are illuminated with integral light in the low‐temperature region a transition from the low‐ohmic state to the high‐ohmic state is observed. The photosensitivity factor grows with the copper doping level. The observed anomalities of transport effects are found to be caused by the presence of a random potential relief in copper‐doped samples. The phenomena of long‐persistent relaxation (LP) and frozen conductivity (FC) are discovered and studied in ZnSe: Cu crystals at 77 K. The γ = E_dr/E_rec value is found to grow with copper concentration in ZnSe, i.e. the recombination barrier grows more slowly than the drift barrier.