At about 1848 Eastern time, the airplane experienced a total loss of power from both engines but was not damaged during a forced landing. Visual conditions prevailed for the Part 135 scheduled domestic passenger flight from Key West, Fla., to Fort Myers, Fla. The airline transport pilot and six passengers were not injured. Before departure, the pilot noted the left and right fuel quantity gauges indicated 300 and 200 pounds, respectively, and took off with each tank feeding its engine. Approaching Naples, the left fuel quantity gauge was still indicating 300 pounds but the left was indicating below 50 pounds. He thought it was an indicator problem. Shortly, the right engine began surging; its fuel gauge was indicating 0, but the left fuel quantity gauge was indicating 300 or slightly more. He moved the right fuel selector to the crossfeed position, which restored engine power. Then, the left engine began surging, followed by the right engine. Unable to maintain altitude he declared an emergency and turned towards Naples. At 3000 feet, he feathered the propellers and lined up for a landing, lowering the landing gear after realizing he could make the runway. He landed, rolling to the end of the runway and onto a taxiway before stopping the airplane. The left main fuel tank contained 275 pounds of fuel as indicated by the fuel quantity gauge and the right main fuel tank contained approximately 13 gallons of fuel. The flexible fuel lines in each engine compartment contained only trace amounts of fuel. Operational testing revealed the left engine quit approximately 15 seconds after the emergency crossfeed shutoff valve was activated or placed in the closed position. With adequate fuel supplied to both engines, no engine discrepancies were noted. The left fuel selector system components were retained for further examination.