The present invention relates to a process for separating at least one first material from a mixture comprising this at least one first material in an amount of from 0.001 to 1.0% by weight, based on the total mixture, and at least one second material, which comprises at least the following steps: (A) contacting of the mixture comprising at least one first material and at least one second material with at least one surface-active substance, if appropriate in the presence of at least one dispersion medium, with the surface-active substance binding to the at least one first material, (B) if appropriate, addition of at least one dispersion medium to the mixture obtained in step (A) in order to obtain a dispersion, (C) treatment of the dispersion from step (A) or (B) with at least one hydrophobic magnetic particle so that the at least one first material to which the at least one surface-active substance is bound and the at least one magnetic particle agglomerate, (D) separation of the agglomerate from step (C) from the mixture by application of a magnetic field, (E) if appropriate, dissociation of the agglomerate separated off in step (D) in order to obtain the at least one first material and the at least one magnetic particle separately.