THE AFT EMER EXIT DOOR WAS NOT CLOSED DURING AN ACR'S TAXI TO THE RWY. THE CABIN CREWMEMBERS CLOSED AND REARMED THE DOOR; AND NOTIFIED THE FLT DECK CREWMEMBERS.

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FLT ON MAR/SUN/95; MSY TO HOU. THE ACFT WAS DELAYED INBOUND. WHEN THE CREW BOARDED THE PLANE; THE CLEANERS WERE ON BOARD. AFTER ARMING THE AFT GALLEY DOOR AND THE TAILCONE DOOR; I WALKED TOWARD THE FRONT OF THE CABIN FOR THE SAFETY DEMONSTRATION. THE FLT ATTENDANTS AT THE FRONT OF THE ACFT WERE POINTING AT ME. I COULD NOT UNDERSTAND WHAT THE PROB WAS. THEN 1 FLT ATTENDANT SHOUTED; 'THE DOOR IS OPEN!' I TURNED AROUND AND SAW THAT THE DOOR TO THE TAILCONE WAS OPEN. I RAN TO THE DOOR AND CLOSED IT. I HAD ARMED THE TAILCONE DOOR BY DROPPING THE FLAP THAT EXPOSES THE EMER HANDLE. AT THAT TIME I DID NOT OBSERVE THAT THE DOOR WAS NOT SECURED. IT APPEARED TO BE CLOSED. SUPPLEMENTAL INFO FROM ACN 299182: I WAS BEGINNING TO READ THE SAFETY DEMONSTRATION WHEN THE B FLT ATTENDANT SAID THAT THE BACK DOOR WAS OPEN; AND QUICKLY STARTED DOWN THE AISLE AND I TURNED AND TOLD THE COCKPIT. ON THE MD-80 THE CLEANERS AND MAINT USE THE TAILCONE STAIRS. WE START DOING OTHER DUTIES AND DON'T NOTICE WHEN THEY LEAVE. THE DOOR CAN BE SHUT AND ARMED; BUT IF IT'S NOT LOCKED; IT WILL SWING OPEN.