A method and an apparatus for determining at least one flow characteristic of an essentially laminarly flowing, gaseous or liquid medium in a pipeline. Distinguishing features include: that at least one modulation element introduced into, or placed in, the pipeline produces, at least for the case, in which the medium is flowing with a velocity different from zero, a change in density of the medium, at least at times, in the vicinity of the modulation element; that at least one mechanically oscillatable unit introduced into, or placed in, the pipeline and spaced from the modulation element is excited to resonant oscillations; that mechanical oscillations are received by the mechanically oscillatable unit and converted into an electrical, received signal, wherein the received signal is sensitive to the density change; and that the at least one flow characteristic of the medium is determined from the reaction of the received signal of the mechanically oscillatable unit to the density change.