Abstract: A cementing system using a tubular member 43 coupled to a string of tubing 14 where upper and lower tubular liner wiper plugs (20, 21) are independently attached to and separately releasable from the tubular member. The upper tubular liner wiper plug 20 has outer liner wiper seal members, an outer latching mechanism (95) and an inner latching mechanism (52). A fluid bypass (59) is located in the liner wiper plug (20) below the wiper seal members with a check valve structure for bypassing fluid from below the seal members to the bore (45) of the tubular member in response to a pressure differential. A second check valve structure (46) is provided in the tubular member to provide a fluid bypass from the exterior of the tubular member above the seal members to the interior of the tubular member in response to a pressure differential.