Flowing fluid may have a chemical composition that changes as a function of time, and this is referred to as slug-flow. To measure the viscosity of the fluid in this scenario requires an instrument with a measurement time less than the time required for one slug to pass through the viscometer. One viscometer that could be used for this purpose is based on determining the damping of the resonance frequency of a vibrating wire. The viscosity can be obtained from measurements of either steady state resonance or amplitude decay. In this article, we report both resonance (that required a data acquisition time of about 40 s) and transient (that required a data acquisition time of about 1 s) measurements obtained with a wire of radius about 0.075 mm immersed in both a stagnant fluid and also when subjected to volumetric flow rates up to 50 cm(3).s(-1). Certified reference materials N35 and S20 were used for these measurements. For both resonance and transient measurements, stagnant N35 was used at a pressure of 0.1 MPa and temperatures between (299.9 and 362.2) K over which the viscosity varied from (2.5 to 66) mPa.s. For flowing fluid, S20 was used at viscosities less than 35 mPa.s. The average absolute difference between the measured and cited values for all measurements was 3.2 %.