A new instrument to carry out complex viscosity measurements in equilibrium and in a steady shear flow has been developed. A small amplitude harmonic excitation is superimposed orthogonally to the steady shear rate component. It is realized by a thin-walled cylinder, which oscillates in the axial direction in a rotating annular cup. The cylinder is suspended from a spring and guided by an air bearing. The spring, which itself is attached to an axially oscillating exciter, has been designed especially for a low linear and a large torsional spring constant. The motion of the cylinder and exciter is recorded and analysed. The applicable frequency ranges from 0.001 up to 50 Hz, the steady shear rate from 0.001 up to 100 s(-1) and the oscillatory shear amplitude from 3 down to 0.003. The temperature can be set and controlled between 5 degrees and 70 degrees C. The instrument is suited for viscosities in the range from 0.3 mPas up to 1 Pas. Considering this, the range and sensitivity with respect to existing instruments has been extended significantly. Besides a description of the instrument much attention has been paid in this paper to the theoretical background of orthogonal superposition in frames of the simple fluid theory. Also the measurement range and calibration of the instrument as well as the accuracy of the obtainable results are discussed. At last some demonstration measurements on both a polymer solution and an ordering latex dispersion are presented.