LANGUAGE BARRIER WITH SOUTH AMERICAN ATC CONTRIBUTES TO TRACK DEV AND ENTRY INTO RESTRICTED AIRSPACE FOR FATIGUED WDB FLT CREW.

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WE WERE 8 MINS BEHIND SCHEDULE WHEN WE ENTERED GUAYAQUIL'S AIRSPACE AT VAKUD INTXN. AFTER MY POS RPT; I REQUESTED 'DIRECT TO UGUPI INTXN' WITH THE CTLR AS THIS WOULD MAKE-UP ABOUT 2 MINS. IN HER BROKEN ENGLISH AND THE POOR RADIO RECEPTION FLYING OVER THE ANDES MOUNTAINS; I THOUGHT SHE SAID WE WERE APPROVED; AND TO RPT OVER GUAYAQUIL VOR. IN HINDSIGHT; SHE SHOULD HAVE TOLD US TO RPT 'ABEAM GUAYAQUIL' AS NEW RTE WOULD TAKE US APPROX 15 MI E OF THE VOR. THIS WAS THE THIRD TIME WE'VE FLOWN THROUGH THEIR AIRSPACE IN THE LAST 48 HRS AND WE WERE GIVEN CLRNC TO DEVIATE THROUGH THE SAME AIRSPACE DUE TO WX OVER GUAYAQUIL. CONSEQUENTLY; I INTERPED THE CHARTED RESTR AIRSPACE; SE(P)-1 AS A 'HOT/COLD' TYPE MIL AIRSPACE WHICH COULD BE TRANSITED WITH CTR'S APPROVAL. THEN AT APPROX XA32Z WE RECEIVED INSTRUCTIONS FROM OUR CTLR TELLING US TO PROCEED DIRECTLY TO GUAYAQUIL VOR (GYV) WHICH WAS APPROX 20 DEGS OFF OUR L AT 40 MI. AFTER WE ENTERED IT INTO THE FMC; AND WERE ESTABLISHED IN THE TURN; HER SUPVR WAS ON THE RADIO TELLING US TO TURN FURTHER L TO A HDG OF 280 DEGS; WHICH WAS AN ADDITIONAL 60 DEGS. THE LIGHT THEN CAME ON THAT WE HAD MISUNDERSTOOD OUR CLRNC TO FLY DIRECT TO UGUPI AND HAD INADVERTENTLY FLOWN APPROX 10 MI ACROSS THE SW EDGE OF RESTR AREA SE(P)-1. AT XA38Z; WE WERE WELL W OF QYV WHEN WE WERE CLRED DIRECT TO UGUPI WITH NO OTHER RADIO COMS UNTIL WE WERE HANDED OFF TO BOGOTA CTL AT UGUPI. I BELIEVE THIS EVENT IS THE RESULT OF POOR RADIO RECEPTION OVER HIGH TERRAIN; THE CTLR'S HVY SPANISH ACCENT; AND CREW FATIGUE. I DISCOVERED THAT THE CAPT AND I WERE ASSIGNED THIS TRIP THAT AFTERNOON WHEN I HAPPENED TO CHK MY MONTHLY SCHEDULE. SCHEDULING CALLED ME AT XA00 LCL AND INFORMED ME WE WERE THE ONLY PLTS AVAILABLE FOR THIS FLT SCHEDULED TO DEPART ZZZ AT XD55 LCL. CLEARLY; I WAS NOT 100% FOLLOWING OUR EARLIER ALL-NIGHT FLT. I WAS TEMPTED TO TELL SCHEDULING THAT I WAS FATIGUED; BUT AS THE CAPT SAID HE WAS GOING TO FLY IT; I DECIDED TO ACQUIESCE FEARING REPERCUSSIONS FROM THE FLT OFFICE. NEVERTHELESS; IF I EVER GET THIS CALL TO FLY BACK-TO-BACK 'ALL NIGHTERS' AGAIN; I WILL CERTAINLY HAVE NO RESERVATIONS THROWING THE 'FATIGUE FLAG;' WE WERE LUCKY WE DIDN'T EXPERIENCE A BA777 TYPE INCIDENT; THIS WOULD HAVE BEEN A LOT WORSE. LESSON LEARNED!