FLC OF A DC10 FAILED TO CONTACT GND CTL PRIOR TO PUSHBACK RESULTING IN TWR STOPPING 2 COMMUTER ACFT FROM ENTERING THE RAMP AREA. SUBSEQUENTLY; AFTER CONTACT WITH TWR; A B767-300 TAXIED PAST THE NOSE OF THE DC10; MISSING BY ONLY A FEW FT; AFTER THE RPTR OBSERVED THE B767 COMING AND THE PUSHBACK TUG DRIVER WAS NOTIFIED TO PUSH THEM BACK FURTHER. THE ACFT DID MOVE BACK A FEW FT BEFORE THE TOW BAR BROKE.

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WHILE SERVING AS FE ON SCHEDULED FLT; WE PUSHED BACK FROM GATE WITHOUT CONTACTING GND CTL. A NOTE WAS MADE BY ME ON THE ATIS CARD INDICATING THAT IT WAS REQUIRED. BOTH THE CAPT AND FO ALSO ACKNOWLEDGED; HOWEVER IN THE ENSUING 'PRE PUSHBACK' FLURRY; THEY FORGOT TO CALL; AND I FORGOT TO REMIND THEM. AT ANY RATE; WE PUSHED OUT AND REALIZED OUR MISTAKE. GND CTL WAS AWARE AND STOPPED 2 COMMUTER AIRPLANES ON THE TAXI. WE APOLOGIZED TO GND AND SPOKE WITH THE SUPVR ON VHF; EXPLAINING THAT IT WOULD NEVER HAPPEN AGAIN. IN THE MEANTIME; HOWEVER; AN ACR Y B767-300 (WHOM WE WERE ALL TALKING TO) TAXIED UP TO THE RAMP ENTRANCE. GND ASKED ACR Y IF HE COULD TAXI BY US INTO HIS GATE; TO WHICH HE REPLIED HE COULD. IT LOOKED TOO CLOSE (AND IT WAS; AS IT TURNED OUT). THE CAPT; FO; AND MYSELF RECOGNIZED THIS. THE CAPT TOLD THE TOW DRIVER TO PUSH US BACK IMMEDIATELY; WHICH HE DID. THE TOW BAR SNAPPED; BUT SERVED ITS PURPOSE AS IT GOT US OUT OF THE WAY. THE ACR Y B767 WINGTIP MISSED US BY 3-4 FT. IT MUST BE POINTED OUT THAT THE 2 SITS WERE UNRELATED. WE WERE ALREADY TALKING TO GND WHEN THEY CLRED ACR Y INTO THE ALLEY. IT IS OUR OPINION THAT THE ACR Y B767 SHOULD NOT HAVE ATTEMPTED TAXIING IN; AS THE SEPARATION WAS INADEQUATE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THAT HE AND THE REST OF THE FLC WERE CONCERNED THAT THE B767-300 DID NOT HAVE SUFFICIENT ROOM TO PASS IN FRONT OF THEIR ACFT AND THAT FO ASKED THE TUG DRIVER TO PUSH THEM BACK FURTHER OUT OF THE WAY. THEN THE CREW HEARD THE TOW BAR SNAP AND BREAK. HOWEVER; THE EXTRA PUSHBACK WAS JUST ENOUGH TO PROVIDE ROOM NEEDED FOR THE B767 TO CLR AS IT PASSED. THE ACFT NOSEWHEEL ASSEMBLY WAS INSPECTED FOR DAMAGE BEFORE TAXIING OUT FOR TKOF. THIS MATTER WAS DISCUSSED WITH TWR SUPVR.