ALTDEV ALT EXCURSION OF ABOUT 900 FT WHEN AN A320 ON APCH DURING A NIGHT OP ENCOUNTERS UNFAVORABLE WX CONDITIONS W OF MMMX.

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I WAS CAPT AND PF WITH LINE CHK AIRMAN (CAPT) IN THE R SEAT ON MMMX CHKOUT. AUTOPLT WAS ON AND WE HAD BEEN LEVEL AT 16000 FT FOR SEVERAL MINS AND DEVIATING FOR NUMEROUS TSTMS AROUND THE ARPT. WE WERE BEING VECTORED TO INTERCEPT THE ARR E OF PTJ AND GIVEN A DSCNT WHEN INCIDENT OCCURRED. WITH AUTOPLT ON; DSCNT TO 12000 FT INITIATED. ACFT WAS IN 'OPEN DSCNT;' BUT CLBED INITIALLY 200 FT. I NOTED THIS TO PNF AND MONITORED SIT. ACFT LEVELED OFF AFTER INITIAL 200 FT CLB AND STARTED SLIGHT DSCNT. ALMOST INSTANTANEOUSLY; LARGE UPDRRAFT OCCURRED AND ACFT PITCHED UP TO 10 DEGS NOSE HIGH AND STARTED TO CLB AGAIN. I IMMEDIATELY TURNED OFF THE AUTOPLT AND FORCED THE ACFT INTO A DSCNT. AT LARGEST POINT OF DEV; ACFT REACHED 16800 FT. AGGRESSIVE DSCNT INITIATED AND DSCNT RESUMED WITH NO OTHER PROBS. SUPPLEMENTAL INFO FROM ACN 623359: DEVIATING AROUND WX ENRTE TO PTJ ON ARR. AUTOPLT ON IN DSCNT AIRPLANE CLBED 900 FT. DISCONNECTED AUTOPLT; STILL UNABLE TO STOP CLB. UNABLE TO NOTIFY ATC DUE TO FREQ CONGESTION. WX WAS DEVELOPING QUICKLY WITH PRECIP AT THE ARPT. NO TFC CONFLICTS AND ATC DID NOT CONTACT US ABOUT THE ALTDEV. WE WERE NOT ABLE TO CONTACT ATC UNTIL WE WERE DSNDING AGAIN ON THE ARR.