ZAN CTLR EXPERIENCED OPERROR WITH 2 SUCCESSIVE DEPS CLBING TO FL260 THE SECOND ACFT FASTER THAN THE FIRST.

Narrative

I HAD JUST STARTED WORKING SECTOR 5R AND D COMBINED. THE AMOUNT OF TFC INCREASED DRAMATICALLY AFTER I SAT DOWN. ACFT WERE DEVIATING AROUND WX BUILDUPS AROUND ANCHORAGE. THERE WERE 2 ACFT XING THE SECTOR (1 LNDG) IN AN UNUSUAL MANNER. 1 ACFT CALLED FOR VFR ADVISORIES BEFORE THE ERROR. THE ERROR: THE 2 ACFT DEPARTED ANC; BOTH SWBOUND; BOTH REQUESTING FL280. AFTER ISSUING THE ALT CLRNC TO BOTH ACFT (THEY WERE SEPARATED BY GREATER THAN 10 MI AT THE TIME); I NOTICED THE OVERTAKE. I ASKED THE REAR ACFT IF HE COULD CLB TO FL300. HE RESPONDED NO BECAUSE HE WAS NON RVSM (HE HAD FILED CONTRARY TO THIS). I CHANGED HIS TYPE/SUFFIX IN THE COMPUTER THEN ISSUED A CLRNC TO THE FRONT ACFT TO MAINTAIN FL260 (THINKING THE REAR ACFT WOULD CLB ABOVE THE FRONT ONE). I WAS DISTR BY SEVERAL OTHER ACFT CALLING (INCLUDING THE VFR POP-UP) AND DID NOT NOTICE UNTIL TOO LATE THAT AN ERROR HAD OCCURRED. I ASKED THE REAR ACFT TO TURN; THEN PUT HIM BACK ON COURSE WHEN I HAD VERT SEPARATION. NO COLLISION ALERT EVER SOUNDED. I TURNED THE ERROR IN TO MY SUPVR AT THIS TIME.