A B727-200 FLT HAS TO DIVERT TO THEIR ALTERNATE ARPT OF ACAPULCO WHEN THE WX IS TOO SEVERE FOR A CONTINUED APCH TO MEXICO CITY. THE FLC HAD GREAT DIFFICULTY IN GETTING THE CTLR TO UNDERSTAND THEIR REQUEST AND THEIR FUEL STATUS.

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UPON ARR IN THE TERMINAL AREA; WX HAD DETERIORATED TO IMC WITH TSTMS IN ALL QUADS. HVY PRECIP; RIME ICE; AND LIGHTNING ENCOUNTERED IN DSCNT. APCH ADVISED US TO EXPECT ILS RWY 23L APCH. THEY RPTED HVY RAIN AT ARPT WITH WINDSHEAR. ADVISED ATC WE WERE BREAKING OFF APCH AND REQUESTED VECTORS TO THE E TO A POINT WHERE WE COULD HOLD UNTIL THE WX IMPROVED. APCH COMPLIED; ENTERED HOLD E OF OTUMBA ON THE 110 DEG RADIAL IN THE CLR. AFTER HOLDING FOR SEVERAL MINS WITH NO IMPROVEMENT IN WX AT ARPT AND WX DETERIORATING AT OUR HOLDING POINT; WE ELECTED TO DIVERT TO OUR ALTERNATE (ACA) FOR FUEL. AFTER SEVERAL VERY FRUSTRATING MINS TRYING TO COMMUNICATE OUR DESIRES; APCH CLRED US DIRECT TO TEQ. THIS RTE RAN DIRECTLY THROUGH WX. ADVISED ATC AND REQUESTED RADAR VECTORS S OF PRESENT POS. AGAIN NUMEROUS ATTEMPTS REQUIRED TO COMMUNICATE DESIRES. FINALLY TOLD ATC FUEL WAS AN ISSUE AND THAT WE WERE REQUESTING RADAR VECTORS DIRECT TO ACA. THEY FINALLY COMPLIED AND WE PROCEEDED TO ACA AND MADE AN UNEVENTFUL VISUAL APCH AND LNDG IN VMC. MAJOR ISSUE WAS LANGUAGE BARRIER. WE WERE ONLY ENGLISH SPEAKING ACFT ON FREQ. COM BECAME DIFFICULT AS WE WERE ASKING THINGS THAT WERE NOT THE NORM FOR ARRS TO MEX. ALSO DIFFICULT TO UNDERSTAND WHAT OTHER ACFT WERE DOING. ATC SEEMED TO FINALLY UNDERSTAND DESIRES WHEN FUEL CONDITION WAS STATED. OUR CONCERN WAS THAT WE MIGHT HAVE UNKNOWINGLY CAUSED PRIORITY HANDLING OF OUR ACFT BY MEXICAN ATC. SUPPLEMENTAL INFO FROM ACN 428508: WE SET UP FOR W LNDG. DSNDING FROM 14000 FT TO 10000 FT; WX GOT WORSE. REQUESTED A FIELD RPT. REPLY WAS NOT UNDERSTANDABLE. NOW WE HAD LIGHTNING -- VIRGA/RAIN; TURB -- LOW VIS/SMOKE OR HAZE -- LIGHTNING IN ALL QUADS -- AND HEARD TWR RPT WINDSHEAR. WE BROKE OFF; CLBED TO FL190; HELD AND REASSESSED. WE HAD FUEL TO GO TO ACA; BUT NOT ENOUGH TO HOLD; WAIT OUT THE WX; SHOOT THE APCH; MISSED AGAIN; THEN GO TO ACA. MEX ATC DIDN'T UNDERSTAND. AFTER MANY ATTEMPTS TO EXPLAIN; WE SAID 'LOW FUEL; MUST GO TO ACA.' SUPPLEMENTAL INFO FROM ACN 428509: DEVS PLUS USE OF ANTI-ICE BURNED MORE FUEL THAN PLANNED. 2 STRONG CELLS WERE DETECTED ON WX RADAR DURING RWY 23 APCH -- 1 N OF MEX AND 1 S. WE BROKE OFF APCH AT APPROX 13 DME. WE CALCULATED FUEL OVER ACA AT APPROX 7000 LBS AND INFORMED ATC WE NEEDED TO FLY TO ALTERNATE OF ACA. NEITHER CAPT NOR FO HAD BEEN THERE. MEX ATC WAS VERY HELPFUL AND OBLIGED OUR REQUEST.