An apparatus for measuring viscosities of fluids is described, comprising: a measuring system (1) having at least one measuring tube (5), which in measurement operation is filled with a fluid or through which fluid is flowing, and which has at least one tube section (4, 7) excitable to execute oscillations; an exciter system (1) for exciting at least two wanted oscillation modes of different frequencies, at each of which at least one of the tube sections (4, 7) is excited to execute oscillations, especially resonant oscillations; a sensing system (3), which is embodied in such a manner that it determines for the wanted oscillation modes excited in measurement operation, in each case, a frequency and a damping, especially a frequency, an amplitude and a damping, of a resulting oscillation of at least one tube section (4, 7) excited to execute oscillations of one of the wanted oscillation modes, and an evaluation system (15), which is embodied in such a manner that it determines based on calibration data stored in a memory (17) for the individual wanted oscillation modes excited in measurement operation, in each case, based on an excitation determined frequency and damping, especially frequency, amplitude and damping, of the resulting oscillation a measured shear rate value and a viscosity measured value, wherein the viscosity measured value corresponds to the dynamic viscosity of the fluid at a static shear rate corresponding to the shear rate value.