FLC OF A CARGO DC8 WAS CLRED ACROSS PARALLEL RWY IN FRONT OF A C150 ON SHORT FINAL. THE CAPT OF THE DC8 EXPEDITED TAXI ACROSS THE RWY; BUT LATER NOTICED THAT THE C150 HAD MADE A GAR.

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UPON CLRING RWY 29 (S SIDE; ACR RWY) S GND CTL WAS CONTACTED. WE WERE CLRED TO TAXI ON PARALLEL; L TURN (N) ON TXWY B; CONTACT N GND (121.9) HOLDING SHORT OF B1. UPON CONTACTING N GND; WE WERE CLRED TO TAXI TO AND HOLD SHORT OF RWY 27L. DUE TO A SLIGHT CURVE; I HELD ABOUT 30 FT SHORT OF THE HOLD SHORT POINT. AFTER A 3-4 MIN DELAY; I WAS CLRED TO CROSS RWY 27L; HOLD SHORT OF RWY 27R. MY EVENTUAL DEST WAS RAMP AREA BY HANGAR; NEARLY 1 MI AWAY. RWYS 27L AND 27R ARE CLOSELY SEPARATED PARALLEL RWYS. PRIOR TO XING RWY 27L; BOTH FO AND I CHKED THE FINAL APCH AREA. A C150 WAS ROLLING OUT ON RWY 27L; A MOONEY WAS ON SHORT FINAL TO RWY 27R AND ANOTHER C150 WAS NOTED ON L BASE BEHIND THE MOONEY. AS I TAXIED PAST THE HOLD LINE; I SAW CESSNA IN A TURN TO FINAL. ABOUT HALFWAY ACROSS RWY 27L; IT WAS OBVIOUS TO ME THAT CESSNA WAS DEFINITELY ON A SHORT FINAL AND LINED UP WITH RWY 27L. I EXPEDITED TAXI AS FAST AS A 230000 LB ACFT COULD BE EXPEDITED. SOME 30- 40 SECONDS LATER; WHILE HOLDING SHORT OF RWY 27R; I LOOKED BEHIND MY L WINDOW AND SAW THE C150 CLBING OUT STRAIGHT AHEAD ON HIS GAR. AS WE WERE ON GND CTL AND NOT TWR FREQ; I DON'T KNOW IF CESSNA INITIATED GAR ON HIS OWN ACCORD OR WAS INSTRUCTED TO DO SO BY TWR. I BELIEVE THAT THIS CONFLICT AROSE EITHER BY MISCOORD BTWN GND AND TWR; OR THE CESSNA MAY HAVE LINED UP WITH THE WRONG RWY; OR WAS CLRED TO LAND ON THE WRONG RWY. HAVING FLOWN INTO LAX SEVERAL TIMES (WHICH ALSO HAS CLOSELY SPACED PARALLEL RWYS) I AM AWARE OF THE IMPORTANCE OF XCHKING ACTUAL TFC WITH ATC XING CLRNCS. THIS BECOMES MORE CRITICAL WITH 'POS AND HOLD CLRNCS;' WHEN YOUR BACK IS TURNED TO LNDG TFC. IN THAT CASE; AT LEAST I'D BE ON TWR FREQ AND ABLE TO MONITOR LNDG TFC CLRNCS; I SUGGEST THAT ACFT TAXIING N OF TXWY B BE CTLED BY N TWR FREQ UNTIL ACROSS BOTH PARALLEL RWYS AND THEN BE HANDED OVER TO GND CTL.