The formation, the reorientation dynamics, and the spatial disorder of easy axis of nematic liquid crystals (LCs) on aligning surfaces are investigated. The first part of the work is devoted to the easy axis formation and its reorientation (gliding) under an external torque on aligning surfaces. The gliding both in azimuthal and zenithal planes is studied. These phenomena are described at molecular level by two processes involving adsorption/ desorption (AD) of LC molecules at the surface and changes of the surface polymer structure. We carried out suitable experiments and proposed a model that allowed us to separate the contributions of these two microscopic mechanisms. In the second part of the work we describe disorder of the easy axis on different anchoring layers. It was found that the statistic characteristics of the disorder have universal features independent on the nature of the aligning layers. We built up a model based on the surface quenching of the nematic orientational fluctuations due to the AD-process which fit reasonably well the experimental results. Finally, we show that the gliding of the average easy axis occurs with a small relative change of its spatial disorder.