FLT ASSIST RECEIVED IN DIVERSION TO ALTERNATE ARPT AFTER INFLT ENG SHUTDOWN AND EMER DECLARED.

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WE HAD PREVIOUSLY FLOWN THE SAME ACFT ON A SGF ROUND TRIP. WITH THE EXCEPTION OF A RECIRCULATION FAN DEFERRAL; ALL ACFT SYS WERE OPERATING NORMALLY. WE DID NOTE THAT THE L ENG ITT WAS RUNNING ABOUT 40 DEGS WARMER THAN THE R; BUT ALL ENG PARAMETERS WERE WITHIN LIMITS. TKOF AND CLB WERE NORMAL. BECAUSE OF HEADWINDS ALOFT; WE REQUESTED AND RECEIVED FROM CTR A CHANGE OF OUR CRUISE ALT TO 16000 FT. A FEW MINS AFTER OUR LEVEL OFF WE HEARD A SUDDEN CHANGE OF ENG SOUND; FELT THE ACFT YAW SUDDENLY NOSE R; AND BOTH SAW THE L ENG TORQUE INCREASE ABOUT 10 TO 15 PERCENT ABOVE CRUISE VALUE. IT REMAINED THERE FOR PERHAPS A SECOND OR SO; THEN DROPPED WELL BELOW CRUISE VALUE. ASSOCIATED WITH THIS DROP WAS A REASONABLY LOUD BANG. A SECOND OR SO LATER THE TORQUE AGAIN OSCILLATED UP; THEN DOWN; ASSOCIATED WITH AN EVEN LOUDER BANG. I DID NOT NOTE THE OTHER ENG PARAMETERS. THE CCAS CRC ALERT; AND ENG #1 'LOW PRESSURE' LIGHT ILLUMINATED. SMOKE IMMEDIATELY BEGAN TO POUR INTO THE COCKPIT. FO AND I IMMEDIATELY DONNED OXYGEN MASKS AND SMOKE GOGGLES; AND BEGAN RUNNING THE APPROPRIATE CHKLISTS. BY THIS TIME; THE SMOKE IN THE COCKPIT WAS SO DENSE THAT; IN ORDER TO SEE THE INSTRUMENTATION; I HAD TO LEAN WAY FORWARD AND GET WITHIN A FEW INCHES OF THE PANEL. WE IMMEDIATELY DECLARED AN EMER AND REQUESTED VECTORS TO THE CLOSEST ARPT. WE RECEIVED VECTORS FOR A L TURN DIRECT COU. WE CONTACTED THE FLT ATTENDANT AND ASKED HIM TO PREPARE THE CABIN FOR AN EMER LNDG. HE INDICATED TO US THAT SMOKE HAD ENTERED THE CABIN ALSO (ALTHOUGH AS HE LATER RPTED; IT WAS MUCH DENSER IN THE COCKPIT). AFTER ACCOMPLISHING THE ENG FLAME OUT AND SINGLE ENG OPS CHKLISTS; THE SMOKE BEGAN THINNING OUT IN THE COCKPIT SO THAT; BY THE TIME WE WERE ON ABOUT A 10 MI FINAL; WE WERE ABLE TO REMOVE THE MASKS AND GOGGLES. FO AND I DISCUSSED THE SIT AND DECIDED THAT; UNLESS WE HAD ANY FURTHER INDICATION OF PROBS; WE WOULD BRING THE ACFT TO A STOP ON THE RWY AND ORDER A PRECAUTIONARY EVAC THROUGH THE MAIN CABIN DOOR ONLY. LNDG WAS MADE WITHOUT INCIDENT; AND FO IMMEDIATELY LEFT THE COCKPIT TO ASSIST WITH THE PRECAUTIONARY EVAC. I RAN THE ON GND EMER EVAC CHKLIST; SECURED THE ACFT; AND EXITED THE AIRPLANE. A FEW PAX SUBSEQUENTLY RPTED SEEING A LARGE FLASH FROM THE L ENG NACELLE AREA ASSOCIATED WITH THE BANGS AND THEN SEEING A LONG TRAIL OF FLAME COMING FROM THE L ENG EXHAUST. AT NO TIME; HOWEVER; DID WE HAVE ANY COCKPIT INDICATIONS OF ENG FIRE. ALL PAX EXITED THE ACFT WITHOUT INCIDENT; AND TO MY KNOWLEDGE; NONE COMPLAINED OF ANY ILL EFFECTS FROM THE CABIN SMOKE OR THE PRECAUTIONARY EVAC.