What was found
(CAN) DURING CLIMBOUT, WITH LANDING GEAR LEVER SELECTED "UP", THE GEAR DOORS OPENED AND GEARS RETRACTED, BUT ALL GEAR DOORS REMAINED OPEN AND THE "LDG GEAR INOPERATIVE" CAUTION ILLUMINATED. THE 3 AMBER "DOOR" ANNUNCIATORS ON THE LANDING GEAR SELECTOR PANEL ALSO REMAINED ILLUMINATED. THE CAPTAIN FOLLOWED HIS QRH, SELECTED THE GEARS "DOWN" AND WHEN IT WAS CONFIRMED HIS GEARS WERE DOWN AND LOCKED, ACFT RETURNED AND LANDED. AN ENGINEER WAS DISPATCHED AND THE PSEU MEMORY WAS INTERROGATED WHICH INDICATED A FAULTY PSEU. THE MEMORY WAS ERASED AND THE PSEU WAS REPLACED AND BITE TESTS CONDUCTED IAW THE AMM. THE ACFT THEN DEPARTED. JUST PRIOR TO DESCENT, THE AMBER "DOOR" ANNUNCIATORS FLICKERED ON AND OFF ABOUT 4 TIMES, TOGETHER WITH A NOISE OF THE DOOR OPENING AND CLOSING FROM THE NOSE GEAR AND THE "LDG GEAR INOP" CAUTION LIGHT ILLUMINATED. THE CAPTAIN DID AN "ALTERNATE EXTENSION" OF THE GEARS AND ONCE CONFIRMED ALL GEARS DOWN AND LOCKED, HE LANDED THE ACFT. ENGINEERS JACKED THE ACFT AND DUPLICATED THIS DEFECT. AFTER TROUBLESHOOTING, RELAY 3261-K11 WAS REPLACED AND THIS RECTIFIED DEFECT.