What was found
PILOT REPORTED 'GEAR UNLOCKED' LIGHT STAYED ON WHEN GEAR SELECTED UP AFTER TAKEOFF. AFTER A FLYBY, TOWER TOLD HIM NOSE GEAR WAS HANGING DOWN, IN TRAIL. PILOT SELECTED GEAR DOWN AND ALL 3 GREEN DOWN AND LOCKED LIGHTS CAME ON AS THE UNLOCKED LIGHT WENT OUT. A NORMAL LANDING WAS MADE AND ACFT TURNED OVER FOR REPAIR. INSPECTED LANDING GEAR RETRACTION SYSTEM AND FOUND BOTH NLG RETRACT ACTUATOR ATTACH LUGS (PN 5713040-22'S) HAD BROKEN WHERE THEY ATTACH TO BOSS OF ACTUATOR. SUSPECT THIS HAPPENED WHEN GEAR WAS SELECTED UP AFTER TAKEOFF AND ALLOWED THE NOSE GEAR TO TRAIL IN THE SLIPSTREAM.