MD80 ENCOUNTERS GRADUAL LOSS OF CABIN PRESSURE. DESCEND IN STAGES TO 10000 MSL AND CONTINUE TO DESTINATION.

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LEVELED OFF AT FL370; HAVING JUST AVOIDED A LINE OF WX E OF SAT; ENRTE TO ATL. NOTICED 'FLOW' LIGHT ILLUMINATED ON OVERHEAD PANEL; ALONG WITH A SMALL CLB RATE ON CABIN VSI. TURNED OFF ENG ANTI-ICE AND GOT SMALL IMPROVEMENT; BUT CABIN CONTINUED TO CLB SLOWLY. DSNDED TO FL330; AND CABIN BEGAN MUCH GREATER CLB WHEN PWR REDUCED FOR DSCNT. LEVEL AT FL330; STILL SLOW CABIN CLB. RAN THROUGH LOSS OF CABIN PRESSURIZATION MEMORY ITEMS AND THEN CHKLIST; WHICH INCLUDED DONNING OXYGEN MASKS. THOUGHT WE MAY HAVE A PACK FAIL; SO DSNDED TO FL250. CABIN CONTINUED TO CLB AND WAS APCHING 10000 FT. GOT CLRNC DOWN TO 11000 FT; THEN 10000 FT AND INITIATED EMER DSCNT PROFILE. GOT TO 10000 FT QUICKLY AND UNEVENTFULLY; WITH MAX CABIN ALT APPROX 11500 FT. PAX MASKS DID NOT DEPLOY. AT 10000 FT; SMALL DIFFERENTIAL PRESSURE WAS MAINTAINED AND CABIN WAS COMFORTABLE AT ABOUT 4000 FT MSL. MADE SURE NO STRUCTURAL DAMAGE WAS EVIDENT; CONFERRED WITH DISPATCH AND MAINT CTL. THANKFULLY; WE HAD A LOT OF FUEL AND WERE ABLE TO CONTINUE TO ATL WITH LEGAL FUEL RESERVES. ON CHKING WITH MAINT AFTERWARDS; SEEMED LIKE A DUCT HAD PARTIALLY RUPTURED DOWNSTREAM OF 1 AC PACK.