ALT EXCURSION ALT DEV BY THE FLT CREW OF AN MU300 DURING AN OVERWATER OP IN A NON RADAR ENVIRONMENT OVER THE GULF OF MEXICO; ON AND OFF FREQ WITH ZHU; TX.

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THE FLT WAS ROUTINE ON THE WAY DOWN TO COZUMEL. WE REFUELED; LOADED OUR PAX AND BEGAN THE FLT TO SAN ANTONIO. OUR ORIGINAL CLRNC WAS UA626; UT11 MAM; BRO; THX; SAT AND CLRED TO FL350. WE EXPERIENCED OCCASIONAL LIGHT CHOP DURING THIS SEGMENT OF THE FLT. THE VISIBILITY WAS UNRESTR AND OVERALL WAS A GOOD RIDE. WHILE ON UT11; WE REQUESTED DIRECT TO SAT. THE CTLR ASKED WE STANDBY AND HE WAS GOING TO CHK WITH ZHU. THE CTLR CLRED US TO SAN ANTONIO AND REQUIRED US TO CLB TO FL410 IN ORDER TO GO DIRECT. THE PIC ACCEPTED THE CLB TO FL410. I ACKNOWLEDGED THE CLRNC WITH CTR AND BEGAN OUR CLB OUT OF FL350. WE TURNED DIRECT SAT AND THE MEXICAN CTLR ADVISED THAT WE WERE OUT OF RADAR COVERAGE AND TO CALL ZHU NW OF ABBOT. I ACKNOWLEDGED AND CHANGED RADIO FREQ TO ZHU. I ATTEMPTED TO CHK IN WITH HOUSTON; BUT NO RESPONSE. WE CONTINUED CLB TO FL410. EVERYTHING APPEARED TO BE NORMAL; AS WE HAVE OPERATED THIS ACFT AT FL410 ON A CONSISTENT BASIS. WE CONTINUED TO EXPERIENCE OCCASIONAL CHOP IN THE CLB. AT ABOUT FL400; THE AIRPLANE BEGAN TO SLOW IN THE CLB TO ABOUT 100 FPM. AROUND FL409; THE AIRPLANE STOPPED CLBING AND THE ONLY WAY TO CONTINUE THE CLB WAS TO CONTINUE TO PITCH THE NOSE UP. HOWEVER; A CONTINUED PITCH-UP WOULD HAVE REDUCED OUR STALL MARGIN AND COMPROMISED THE SAFETY OF THE AIRPLANE; CREW AND PAX. WE STAYED LEVEL AT FL409 FOR A FEW MINS; BUT DUE TO THE OCCASIONAL CHOP THAT WE EXPERIENCED; IT WAS DECIDED BY BOTH FLT CREW MEMBERS THAT THE SAFEST COURSE OF ACTION WAS TO DSND TO FL390 SO THAT THE STALL MARGIN WAS NOT COMPROMISED. AT THIS TIME; I ATTEMPTED TO CALL ZHU TO ADVISE THAT WE NEEDED TO DSND TO FL390. I MADE NUMEROUS ATTEMPTS. I WENT BACK TO THE MEXICAN CTR FREQ AND ATTEMPTED CONTACT; BUT THE SAME RESULT -- NO RESPONSE. AT THIS POINT; WE BEGAN A DSCNT TO FL390 WITH CONTINUED CALLS TO ZHU. ALSO; THERE WAS ANOTHER AIRLINE FLT THAT WE COULD HEAR AND WE ATTEMPTED A RELAY VIA THEM; TO ADVISE HOUSTON OF OUR INTENTIONS TO GO TO FL390. WE NEVER HAD THEM ACKNOWLEDGE OUR REQUESTS FOR RELAY. AFTER LEVELING AT FL390; ANOTHER ATTEMPT WAS MADE TO ZHU WITHOUT A RESPONSE. ABOUT 1-2 MINS LATER; WE COULD HEAR ZHU TALKING TO ANOTHER ACFT. I CALLED HOUSTON TO CHK IN AT FL390. HOUSTON RECEIVED OUR CALL; BUT THE CTLR WAS CONFUSED WHY WE WERE AT FL390. HE ADVISED THAT WE WERE CLRED TO FL410. I ACKNOWLEDGED AND ADVISED THAT WE WERE UNABLE TO MAINTAIN FL410 AND WE HAD TO DSND TO FL390. HE WORKED A FEW OTHER ACFT AND CAME BACK TO ASK HOW LONG WE WERE AT FL390. I ADVISED THAT IT WAS ONLY FOR A FEW MINS. HE ASKED FOR OUR POS. I ADVISED OF OUR LOCATION. HE ASKED HOW LONG BEFORE REACHING SAN ANTONIO. I ADVISED TIME ENRTE. HE ADVISED THAT THERE WERE 2 OTHER ACFT IN THE SECTOR AND THAT THERE IS NO RADAR COVERAGE IN THE AREA. I ACKNOWLEDGED AND ADVISED THAT WE HAD TO DSND. WE WERE HANDED OFF TO ANOTHER CTLR AND THE FLT CONTINUED NORMALLY TO SAN ANTONIO. DURING THE DSCNT; THE VISIBILITY WAS UNRESTR AND THE FLT CREW MADE A CONTINUOUS SCAN FOR OTHER TFC. THE ELAPSED TIME FROM FL410 WAS ONLY A MATTER OF MINS. THE TIME TO REACH ZHU AFTER THE LEVEL OFF WAS ALMOST SIMULTANEOUS.