CPR LTT SPD DEV CAUSES LTSS WITH ACFT COMING UP FROM BEHIND WHILE ON STAR INTO LGA.

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WE HAD BEEN CLRED BY WASHINGTON CENTER TO FLY THE NANCI 4 STAR TO KLGA AND MAINTAIN 300 KTS OR BETTER. WE WERE NEAR THE BARBER POLE AND THUS TOLD ATC THAT 300 KTS WOULD BE OUR MAX. AFTER SWITCHOVER TO NY CENTER WE WERE CLRED TO DSND AND CROSS SOMTO INTXN AT 11000 FT. NEARING 12000 FT WE HEARD CENTER TALKING TO AN MDT BEHIND US ABOUT HIS AIRSPD. THEN ATC ASKED US FOR OUR AIRSPD. WE TOLD HIM 250 KTS AND HE STATED (NOT VERBATIM); IMMEDIATELY INCREASE TO 300 KTS; THAT WE HADN'T BEEN CLRED TO DECREASE BELOW 300 KTS; THAT WE'D ALMOST BEEN RUN OVER; AND THAT HE WOULD HAVE TO WRITE UP THIS ONE. WE IMMEDIATELY ACCELERATED TO 300 KTS AND CONTINUED TO AN UNEVENTFUL APCH AND LNDG AT KLGA. THE PF HAD SLOWED TO 250 KTS AS HE HAD UNDERSTOOD THE CLRNC TO BE 11000 FT AND 250 KTS OVER SOMTO. AS CAPT BUT PNF; I WAS NOT MONITORING AIRSPD CLOSELY AT THE TIME. I DID NOT CONSIDER 250 KTS TO BE UNUSUAL OR SLOW AS WE WERE NEARING THE NEW YORK CITY AREA AND WOULD BE SOON DSNDING BELOW 10000 FT. NOR CAN I CONFIRM THERE WAS ANY AIRSPD RESTRICTION OVER SOMTO. WASHINGTON CENTER HAD MADE THE 300 KT REQUEST AND I DIDN'T QUESTION IF NY ATC HAD CHANGED OR RESTATED A SPECIFIC AIRSPD. I DO QUESTION WHY THE ATC GND EQUIP AND PERSONNEL (ATC SYS) ALLOWED 2 ACFT TO GET SUFFICIENTLY CLOSE TO WARRANT CTLR REMARKS AS PREVIOUSLY STATED. A CONTRIBUTING FACTOR TO OUR SLOWING TO 250 KTS WAS A CONDITIONED REACTION BY OUR OPS IN THE STL AND ORD AREAS. IN THOSE 2 AREAS; AS AT SOME OTHERS; A CLRNC TO 12000 FT IS USUALLY ACCOMPANIED BY A 250 KT AIRSPD RESTRICTION. THIS; OF COURSE; IS NO EXCUSE TO CHANGE AIRSPD ON ALL DSCNTS. WE HAVE OPERATED IN THE NE CORRIDOR BEFORE; BUT THIS OCCURRENCE POINTS OUT THAT WE MUST REMAIN EVER VIGILANT AND ALERT AT ALL TIMES AND HEIGHTEN OUR AWARENESS IN HIGH DENSITY TFC AREAS.