A B767-300'S R MAIN GEAR WOULD NOT RETRACT. THE CREW CONTINUED A SHORT FLT TO THE ACFT'S INTENDED DEST.

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STANDARD NOISE ABATEMENT WITH GEAR UP AT POSITIVE CLB AND VNAV AT 800 FT. WE GOT THE GEAR DOOR EICAS AND THE GEAR DOOR AMBER LIGHT WHILE THE GEAR WAS RETRACTING AND THEN THE GEAR DISAGREE EICAS AND AMBER LIGHT WHEN THE GEAR SEEMED TO BE UP. THE COPLT WAS FLYING AND HE HAD SELECTED LNAV FOR LATERAL GUIDANCE. AFTER FLAP RETRACTION I SAID I WOULD PUT THE GEAR BACK DOWN AND SEE IF THE PROB WOULD GO AWAY. I MOVED THE GEAR HANDLE FROM UP TO DOWN AND WE GOT THE GEAR EXTENSION WITH 3 GREEN GEAR LIGHTS AND NOW ONLY HAD THE GEAR DOOR EICAS AND GEAR DOOR AMBER LIGHT. I THEN MOVED THE GEAR HANDLE TO UP AND ALL 3 GREEN LIGHTS WENT OUT BUT THE GEAR DISAGREE EICAS AND GEAR DISAGREE AMBER LIGHT RETURNED. THERE WAS AN OBVIOUS RUMBLE SIMILAR TO GEAR BEING DOWN. I MOVED THE GEAR HANDLE TO OFF AND THE R MAIN GEAR GREEN LIGHT CAME ON. THE COPLT SAID HE WOULD HANDLE THE RADIOS AND I GOT OUT THE FLT MANUAL AND WENT THROUGH GEAR DOOR AND GEAR DISAGREE PROCS. AFTER I READ THEM ALOUD THE COPLT AND I HAD A DISCUSSION ABOUT WHERE TO GO AND SINCE WE ONLY HAD 180 OR SO TOTAL MI POINT TO POINT AND WE WERE NOW AT BOTTOM INTXN THERE WAS JUST UNDER 100 MI TO GO. WE PUT OUR SPD IN THE FMC AS WE DECIDED NOT TO GO FASTER THAN 250 KTS AND IT APPEARED TO BOTH OF US THERE WAS ADEQUATE FUEL TO GO TO ZZZ AND RETURN TO ZZZ2 IF NECESSARY. I ADDED THAT ZZZ HAD BETTER MEDICAL FACILITIES SHOULD WE ENCOUNTER A PARTIAL GEAR SITUATION. WE BOTH AGREED THAT ONCE WE PUT THE GEAR DOWN WE WOULD HAVE A SAFE GEAR INDICATION AND WOULD BE ABLE TO ACCOMPLISH A NORMAL LNDG. WE ALSO AGREED THAT NOWHERE HAD THE PROC TOLD US TO LAND AT THE NEAREST SUITABLE ARPT. WE CONCLUDED BECAUSE WE FELT WE DID NOT HAVE AN UNSAFE SITUATION TO CONTINUE TO ZZZ AND CONTACT DISPATCH AND MAINT FOR FURTHER INFO AS OUR ACARS WAS OUT AND I WAS CONCERNED ABOUT THE WX AT ZZZ AS THERE WAS TSTMS IN THE FORECAST. AFTER CONFERENCE OUR DECISION REMAINED CONTINUE TO ZZZ AS THE WX WAS GOOD AT THE ARPT AND OUR RADAR NOW WAS SCANNING ALL AREAS 80-160 MI AROUND ZZZ. OUR INTERP ALSO CONCLUDED WX COULD BE CIRCUMNAVED AND ARR AND LNDG WOULD BE IN GOOD WX. AS I RETURNED TO THE FLYING LOOP THE COPLT HAD RECEIVED HOLDING INSTRUCTIONS AT USABA INTXN (80 MI FROM ZZZ). I TOLD DISPATCH AND MAINT TO STAY ON THE HOOKUP AS MORE MAY DEVELOP. THE HOLD WAS GIVEN WITHOUT AN EFC AND WE DISCUSSED AT WHAT POINT WOULD WE CHANGE OUR DEST TO ZZZ2. WE AGREED 18 OR 19000 LBS WOULD BE REQUIRED. OUR HOLD TURNED OUT TO BE A FEW TURNS AND THEN VECTORS TO FINAL APCH. WHEN ASKED ATC TOLD US WE WERE #6 I ELECTED TO TELL THEM WE WERE MINIMUM FUEL AND COULD NOT ACCEPT UNDUE DELAYS. THE CTLR HANDED US OFF AND SAID THE NEXT CTLR KNEW OF OUR FUEL SITUATION AND IT APPEARED WE WERE IMMEDIATELY VECTORED FROM A WESTERLY HDG TO A NE HDG TO INTERCEPT LOC. THE GEAR EXTENSION WAS AS EXPECTED AND ONLY THE DOOR MESSAGE AND LIGHT REMAINED. THE LNDG WAS NORMAL AND EVEN THE DOOR MESSAGE AND LIGHT WENT OUT. MAINT; FLT OPS DUTY MGR AND UNION ALL BRIEFED AFTER BLOCK-IN.