The invention relates to a method for processing a substance or substance mixture which is situated in a container and rotates about the container axis, notably because of a mixing or stirring action. Owing to the disadvantages inherent in the prior art, the aim of the invention is to create a method which permits the gentle treatment of a fluid substance or substance mixture, by means of which the necessary energy can be introduced into the mixture without adversely affecting the quality thereof and which satisfactorily solves the problem of heat transfer without the need for complex technical apparatus. To this end the invention provides for substances located in the container (1) to be withdrawn from the container in the direction of their tangential speed component at a point (6) on the outer circumference of said container and to be returned to the container at a different point (12) of the container (1) in a direction of flow which is not opposite to the tangential speed component of the substances located in the container (1) at the point at which the substances are returned. The dynamic pressure difference between the withdrawal point (6) and the return point (12) in the container (1) is used to transport the substances circulating therein. Said dynamic pressure difference is obtained substantially from the tangential speed component acting at the withdrawal point (6).