A B737-200 FO RPTED THAT ZME WAS CONCERNED WITH SLIGHT TRACK DEVS THE ACFT MADE; AS WELL AS THE LOST COM FOR 80 NM; WHILE FLYING AT FL310.

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AT FL310; WE RECEIVED AN ACARS MESSAGE FROM COMPANY ASKING US TO CONTACT ZME. WE CHKED IN AND WE WERE TOLD TO IDENT. WE DID AS INSTRUCTED. ATC ACKNOWLEDGED OUR CHK-IN AND ASKED US TO IDENT AGAIN. AGAIN; WE IDENTED; AND THIS WAS FOLLOWED BY ANOTHER REQUEST TO IDENT. CAPT ASKED IF THERE WAS A PROB. THE CTLR SAID THAT WE HAD BEEN NO-COM FOR 80 MI AND SAID THAT THE ACFT HAD MADE SEVERAL SLIGHT TURNS. CAPT INFORMED HIM THAT WE HAD NOT RECEIVED A HDOF AND THE ACFT WAS TRACKING THE RADIAL AND MAKING THE TURN OVER THE VOR. WE ASSUMED THEY DID NOT REALIZE WE WERE 'SLANT ALPHA;' AND CONTINUED TO FLY. THE CTLR THEN ASKED WHETHER THE COCKPIT DOOR WAS SECURE. WE INFORMED HIM THAT IT WAS. THE CTLR SAID THAT PHONE CALLS HAD BEEN MADE. BOTH THE CAPT AND MYSELF ASSUMED THAT THIS HAD GENERATED THE ACARS MESSAGE. THIS IS NOT THE FIRST INCIDENT WITHIN THIS RADAR SECTOR. A SIMILAR EVENT HAPPENED IN MAR/04. THE CTLR TOLD US IT HAD BEEN A LONG DAY. I ALSO BELIEVE THAT THE CTLRS HAVE BECOME COMPLACENT WITH MOST ACFT BEING RNAV EQUIPPED. I HAVE BEEN CLRED TO INTXNS REPEATEDLY WITHOUT THE EQUIP TO COMPLY. THE B737-200 IS THE ONLY SLANT ALPHA EQUIPPED ACFT.