A B737-300 TAXIING FOR TKOF AT RENO HAD TO STOP TAXIING BECAUSE THEY WERE NOT SURE IF A DC8 WOULD TURN INTO THEM FROM A PARALLEL TXWY.

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AFTER DISCONNECTING FROM AN EXTENDED COM WITH OUR PUSHBACK CREW ON THE TERMINAL RAMP; I ASKED THE FO TO RECONFIRM OUR TAXI CLRNC WITH GND AS I HAD MISSED THE RESPONSE TO HIS FIRST CALL. WE WERE CLRED TO 'RWY 16R VIA TXWYS A; G; AND B.' AFTER TURNING NBOUND ON TXWY B; WE WERE PARALLELING A DC8 THAT WAS NBOUND ON TXWY A. APCHING INTXN D; THE FO SWITCHED TO TWR FREQ AS WE WOULD BE #1 FOR TKOF. AT THAT TIME THE DC8 STARTED A TURN EBOUND ON TXWY D; RIGHT TOWARD OUR TAXI PATH/RTE. BOTH ACFT THEN CAME TO A STOP SO AS NOT TO SHARE THE SAME POS ON THE TXWY INTXN. WE THEN CONTINUED THROUGH THE INTXN TO RWY 16R; WERE CLRED FOR TKOF; AND DEPARTED. NO MENTION WAS HEARD FROM TWR AT ANY POINT ABOUT THE DC8 TAXI TFC. NO MENTION WAS MADE FROM GND CTL EITHER AFTER OUR TAXI CLRNC WAS RECEIVED. PERHAPS THE DC8 WAS HOLDING SHORT OF TXWY B ANYWAY; AND I WAS SIMPLY UNAWARE OF HIS CLRNC. PERHAPS GND CTL MADE MENTION OF THE DC8; BUT WE HAD ALREADY SWITCHED TO TWR FREQ. RECURRENCE COULD BE PREVENTED BY: 1) GND CTL ISSUING TFC/SEQUENCE AFTER OUR ORIGINAL CLRNC TO TAXI. 2) STAYING WITH GND CTLR UNTIL PHYSICALLY AT THE DEP END OF THE RWY; INSTEAD OF JUST APCHING IT.