A method of monitoring the condition of a pump (10) or at least one component of a system that includes a pump which component or components are not a part of the pump, includes the step of generating a predetermined test condition in the pump or system component or components. During a period in which such a test condition is present, signals indicative of the pump or system component or components are obtained. Wear in the pump bearings, the build-up of deposits in the pump or in pipework forming a part of the pump system can be detected or predicted and corrective action taken before the pump or system fails. By providing a method of monitoring pump or system condition in-situ, it is possible to reduce the likelihood of pump failure in use and the need to carry out over frequent servicing of the pump.