This article deals with the integrated holistic modelling of 5-axis high-speed machining centres and the main error sources located in the rotating control axes. A strategy for reducing and effectively compensating thermal errors is presented. The strategy includes steps of error recognition based on knowledge, modelling, numerical simulation analysis and mutual interactions. A holistic hybrid model of spindle axial displacements caused by high spindle rotational speeds is described. Attention is given to the modelling of displacements arising in the spindle assembly (due to centrifugal forces) and in the tilting table with direct drives in axes A and C. The conditions that the prognostic modelling of thermal errors must satisfy to ensure the effective compensation of the latter are discussed and error identification methods are presented.