NMAC BTWN A DC10-10 JUST LIFTED OFF ON AN INITIAL CLB; AND OVER AN INTERSECTING RWY; AND A B737-200; AT 150 FT ABOVE THE DC10 AND XING OVER THE TOP ON INITIAL CLB AFTER TKOF ON THE INTERSECTING RWY. EACH RWY WAS ON DIFFERENT CTL FREQ. TWR ADMITTED LATER THAT BOTH ACFT HAD BEEN CLRED FOR TKOF AND THAT IT WAS AN ATC OPERROR.

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TAXIING FOR TKOF AT LAS RWY 25R. WHILE ON TXWY B PASSING A2 THE FO CONTACTED THE TWR ON 119.9 AND WE WERE CLRED FOR TKOF RWY 25R. CHKLISTS WERE COMPLETED AND THE CAPT COMMENCED TKOF ROLL APPROX 2 MINS AFTER THE TKOF CLRNC WAS RECEIVED. THE ACFT WAS ROTATED AT APPROX 165 KTS. THE CAPT CALLED FOR THE GEAR TO BE RAISED. AS THE FO REACHED FOR THE GEAR HANDLE HE LEANED FORWARD SLIGHTLY. OUT OF THE FO'S CLR VIEW SLIDING WINDOW; I SAW A B737 IN A CLB ATTITUDE AT ABOUT THE 1:30 O'CLOCK POS; RELATIVE TO US; CONVERGING. WE BOTH CROSSED THE INTXN OF RWYS 25R AND 19 SIMULTANEOUSLY. I ESTIMATED THE B737 TO BE APPROX 150 FT ABOVE. I COULD NOT TELL EXACTLY BUT BELIEVE THE B737 PASSED OVER US OR SLIGHTLY BEHIND. THE INCIDENT WAS OVER BEFORE I COULD ALERT THE OTHER CREW MEMBERS. NEITHER THE CAPT OR FO SAW THE B737. I CALLED OUT 'WOW; DID YOU SEE THAT B737.' THE FO QUESTIONED WHAT I HAD SAID; AND I TOLD HIM WHAT I HAD SEEN. I THEN SAID LOOK AT THE TCASII. THE TCASII ON THE 10 MI RANGE SHOWED AN AMBER WITH +2 VIRTUALLY ON TOP OF OUR ACFT SYMBOL. THE CAPT CALLED THE TWR. THE TWR SAID THEY WERE CHKING TO SEE WHAT HAD HAPPENED; AND TOLD THE CAPT TO CONTACT DEP. DEP CALLED 'TFC AT 7 O'CLOCK POS; DO YOU HAVE IT IN SIGHT?' (I DON'T RECALL THE DISTANCE.) WE DID NOT HAVE THE TFC. 3 MI W; THE CAPT BEGAN A L TURN AS PUBLISHED ON THE SID. DEP AGAIN CALLED OUT THE TFC AND ISSUED US A HDG OF 210 DEGS. WE NOW HAD THE TFC IN SIGHT AT 9 O'CLOCK POS; PARALLELING OUR TRACK APPROX 3 MI. NO FURTHER INCIDENT. THE CAPT ELECTED TO HAVE THE VOICE RECORDER CIRCUIT BREAKER PULLED TO SAVE THE TAPE. WE WERE LATER INFORMED BY OUR FLT OPS THAT THE TWR HAD CLRED BOTH ACFT FOR TKOF. CONTRIBUTING FACTORS: LAS HAS DIFFERENT TWR FREQS FOR THESE INTERSECTING RWYS: RWY 25R -- 119.9 AND RWY 19 -- 118.75. SUGGESTED CORRECTIVE ACTION: INTERSECTING RWYS SHOULD ALWAYS BE ON THE SAME FREQ.