We present new results of experimental investigations of azimuthal director reorientation dynamics for a nematic liquid crystal on solid substrates. Two types of substrate with weak anchoring were studied: glass/polystyrene and glass/UV‐activated dye. Slow and fast relaxation processes were observed in both cases under the action of a strong ‘in‐plane’ electric field. The slow surface reorientation and memory effects were controlled by two parameters: the electric voltage and the excitation time. It was established that the increase of the excitation time results in a slowing of the relaxation of the system to the initial state after turning off the electric field. A phenomenological model of a gliding of easy axes is proposed to explain the slow relaxation process.