A chain scraper conveyor has a conveyor line of linked segments so as to be curvable. A scraper chain runs in a conveying channel through the conveyor line. The scraper chain turns around chain drums in machine frames at the ends of the line, these being drivable to circulate the scraper chain and/or longitudinally adjustable to tension it. The conveyor has wheels so as to be bodily movable, e.g. by an integral caterpillar-track drive at one end, and for this reason includes a flexible tension element, preferably a round-link chain, that extends along the conveyor line under the channel and is fixed at its ends. The tension chain has lateral freedom relative to the segments, limited by side abutments. At curves (A, B) it can take up a substantially chordal relation to the center line of the conveyor so as to reduce stress on the scraper chain and the consequent tendency of the line to straighten out when being driven.