BEECH 1900D FLC WHEN TURNING AROUND ON THE RWY TO BACK-TAXI NOTICED AN RV3 ACFT LAND FROM THE OPPOSITE END COMING TOWARD THEM AND THEN TURN OFF THE RWY AT THE MAIN TXWY. HE DID NOT ATTEMPT TO GO AROUND AFTER SEEING THE RWY OCCUPIED; NOR MAKE ANY CALLS ON HIS RADIO OF HIS INTENTIONS.

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ON A VISUAL APCH TO LARAMIE ARPT; APCHING FROM THE S; FO MADE TFC CALLS 20; 10; AND 5 MI OUT ON CTAF WHILE CAPT WAS FLYING. WERE INFORMED BY LAR UNICOM THAT AN EXPERIMENTAL ACFT (RV3) WAS MAKING TOUCH-AND-GOES ON RWY 12; BUT WAS NOT XMITTING ON CTAF OR UNICOM. ACFT WAS NOT APPEARING ON TCASII. DECIDED TO FLY A HIGH L DOWNWIND UNTIL ACFT WOULD BE IN SIGHT. ENTERED L DOWNWIND FOR RWY 12 WHEN FO SPOTTED ACFT TAKING OFF FROM RWY 12. VISUAL SEPARATION WAS ASSURED AND PERFORMED NORMAL LNDG ON RWY 12. OTHER ACFT WAS STILL NOT MAKING ANY TFC CALLS. AFTER MAKING A STOP ON RWY 12; WE ADVISED THAT WE WOULD BACK-TAXI TO RWY 12 TO TXWY B TO EXIT RWY (AS IT WAS ONLY TXWY PRACTICAL). AS WE TURNED OUR ACFT AROUND; WE NOTICED THAT THE RV WAS PERFORMING A LNDG ON RWY 12 WHILE WE WERE STILL ON THE RWY. WE HOPED THE ACFT WOULD PERFORM A GAR; BUT DID NOT. THE RV LANDED ON RWY 12 WHILE WE WERE STILL ON IT FACING ITS OPPOSITE DIRECTION. THE RV THEN EXITED ON TXWY B. MADE NO TFC CALLS. WE THEN BACK-TAXIED ON RWY 12 AND TXWY B FOR THE TERMINAL. CAPT DECIDED TO GO TALK TO PLT OF RV. THE RV PLT STATED THAT HE SAW US ON THE RWY; BUT DECIDED TO LAND ANYWAY. I NOTICED THAT HE WAS RADIO EQUIPPED. RV PLT SEEMED UNAWARE OF BASIC VFR TFC REGS AT UNCTLED ARPTS.