Abstract: An apparatus for measuring the viscosity and temperature of a fluid, for example an engine oil, comprises a transducer, which is arranged to vibrate when provided with a drive signal to produce an ultrasonic shear wave; an impedance matching layer that is inserted into the fluid and which couples at least a portion of the ultrasonic waves produced by the transducer into the fluid and from which at least a portion of the wave is reflected back to the transducer; a detector which is adapted to detect a measurement signal produced by the transducer when the reflected wave is incident upon the transducer; a control circuit which varies the frequency of the drive signal applied to the transducer and hence the frequency of the ultrasound signal; a processing means which determines the optimum frequency of the drive signal at which the measurement signal output from the transducer has its minimum amplitude; and a temperature determining means which estimates the temperature of the fluid as a function of the optimum