The mixing process in the homogenisation of liquids is considered. The mixing may be carried out in dynamic and static mixers. The stirred vessel and the reciprocating-jet-reactor belong to the group of dynamic mixers. The stirred vessel is the most widely applied mixer, while the reciprocating-jet-reactor is quite an innovative one, the design of which is based on the results of the fundamental research on the mixing process in stirred vessels. The reciprocating-jet-reactor consists of a slender cylindrical vessel in which a package of plates is forced into a reciprocating motion. By this motion the fluid is pressed jet-like through a targe number of holes. When the moving plate package changes its direction, so the jet-streams. Both types of dynamic mixers are characterized by a typical moving element, which produces a kind of fluid now favourable to the mixing of the fluids concerned. In contrast to dynamic mixers, the desired fluid flow in static mixers is produced by a pump that is arranged outside of the mixing system. The fluids introduced into the static mixer are split up in thin layers and periodically separated and brought into contact again under new conditions. In static mixers the mixing process is predetermined. In this investigation, only the two dynamic mixers mentioned above are considered. The method applied is a strictly theoretical one. The fundamental differential equations for the velocity field and the temperature as well as the concentration field have been solved by numerical methods. While fluid now has been assumed to be time-independent, temperature and concentration field have been considered as a function of time. In this way, the mixing time could be determined. Analysis of the fluid dow in conventional mixing vessels proved that the rotational primary flow does not have any influence on the mixing process, although the fluid now consumes most of the energy transferred to the fluid by the rotating stirrer. Mixing of the fluids is practically due only to the secondary now, which is initiated by centrifugal forces resulting from rotational primary motion. As a consequence, it seems advisable to avoid rotational fluid motion in mixers. The mixing process in stirred vessels may be divided into three ranges of the Fourier number, Fo. In the range of small values of Fo the process is determined by molecular transport of mass due to concentration gradients in time. Convection has no decisive influence on mixing. The influence of convective mass transport is observed only in an intermediate range of the Fourier number. In this range, the temperature and the concentration field gradually assume the same structure as the velocity field of the secondary now. When the identity of both fields is attained, molecular transport has again the dominating influence on the mixing process. In the reciprocating-jet-reactor unusually short mixing times are obtained due to periodic changes of the jet flow direction. An analysis of the mixing process showed again three ranges of the Fourier number with different influence of molecular transport and convection. In this case, however, molecular transport is very strong, because of the steep concentration gradients during variation of flow direction of the jets.