A buffer store for a flat web material includes two roller registers having freely rotatable rollers movable relative to one another in a direction radial to a roller axis, thereby forming loops of the web material between the rollers, a piston-cylinder arrangement having a chamber containing a compressible medium and acting as a spring between the registers to generate web tension in the material, and a control-valve arrangement that switches between a first condition, for normal operation, and a second condition, for operation during a fault. In the first condition, the control-valve arrangement connects the cylinder chamber of the piston-cylinder arrangement to a device for providing a constant operating pressure. In the second condition, the control-valve arrangement closes the cylinder chamber of the piston-cylinder arrangement and connects it to a relief valve that relieves pressure therein to a residual pressure significantly smaller than the operating pressure.