An apparatus for determining and/or monitoring volume- and/or mass-flow of a medium flowing through a pipeline in a stream direction. At least two ultrasonic sensors are included, which are secured in a defined measuring positional relationship on the outer wall of the pipeline and alternately emit and receive ultrasonic measuring signal. A control/evaluation unit, which determines volume- and/or mass-flow of the medium in the pipeline on the basis of the travel time difference of ultrasonic measuring signals in the stream direction and opposite to the stream direction is also provided. For assuring rapid mounting and demounting of the ultrasonic flow measuring device on a pipeline, the at least two ultrasonic sensors are secured on a pliers-like clamping unit, which is embodied in a manner such that the ultrasonic sensors are brought into a measuring positional relationship by simple clamping onto the pipeline.