Abstract: A method and apparatus for pumping fluids, especially viscous and/or abrasive fluids, are disclosed. The method comprises using one working fluid to pump an intermediate working fluid, which may be different from the first working fluid, through a conduit system in a smooth and continuous pulsating manner. The intermediate fluid pumps the process fluid through the actual pumping zone. Heat exchange between the intermediate and process fluids may be effected, e.g. by counterflow. The preferred apparatus comprises a hydraulically operated displacement pump. A tubular diaphragm pump is coupled in-line in a pipe line. The tubular diaphragm pump includes a housing coupled to the pipe line, and a tubular diaphragm coupled to the housing in such a manner that the process fluid flows from the pipe line, through the interior of the tubular diaphragm and back into the pipe line. A check valve insures that the process fluid passes through the tubular diaphragm in a single direction.