LEAR 35 AIR TAXI CARGO ACFT HAS NMAC DURING INITIAL CLB ON IFR FLT PLAN.

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ARPT: PWT. ACFT: LEAR 35. WX CONDITIONS AT TIME OF ARR AND DEP: A SCATTERED TO BROKEN LAYER OF STRATUS CLOUDS AT 600 FT AND THE VISIBILITY WAS BTWN 7 AND 10 MI AS PER THE AWOS-3 ON 121.2. IFR CLRNC ISSUED FOR DEP: AFTER DEP; TURN TO A HDG OF 160 DEGS FOR VECTOR TO JOIN THE SEATTLE 227 DEG RADIAL TO THE ELMAA INTXN; J 589 TO CORVALLIS; THEN AS FILED; MAINTAIN 5000 FT; EXPECT 15000 FT WITHIN 5 MINS AFTER DEP. THIS CLRNC WAS GIVEN TO US WHILE ON THE GND; JUST PRIOR TO ENG START VIA SEATTLE APCH WHICH I RECALL TO BE ON 127.1. BEFORE USING THE CLRNC; WE WERE ASKED WHICH RWY WE PLAN TO DEPART; OUR ANSWER; RWY 19. MORE FACTS ABOUT PWT: THE ONLY ADVISORY FREQ IS 'THE PORT OF BREMERTON' ON 122.7; 24 HRS PER DAY. THE ELEVATION IS 439 FT AND THE RWY IS 19/01; 6200 FT LONG; 1500 FT WIDE AND IS SERVED WITH AN ILS AND AN NDB APCH. THE APCH LIGHT SYS IS ACTIVATED BY KEYING THE ACFT XMITTER ON 122.7. SEQUENCE OF EVENTS: AFTER THE CLRNC TO LOS ANGELES WAS COPIED AND READ BACK; THE PHRASE CAME BACK FROM SEATTLE; 'YOU ARE RELEASED AT THIS TIME.' WE ANNOUNCED ON 122.7 THAT 'FLT WAS TAXIING ON OUT TO RWY 19 AT BREMERTON FOR DEP.' FOR THIS LEG FROM BREMERTON TO LOS ANGELES; I WAS FLYING. DURING THE TAXI-OUT; I REMEMBER MENTIONING TO MY FO THAT -- 'WE'LL BE SURE TO GIVE A CALL TO BOTH THE PORT OF BREMERTON AND TO SEATTLE JUST PRIOR TO STARTING THE TKOF ROLL.' BY THE TIME WE REACHED THE APCH END OF RWY 19; WE HAD COMPLETED THE QUICK TURN CHK AND WE WERE READY FOR DEP. A VERY SHORT TIME -- (PROBABLY 30 SECONDS) BEFORE TAXIING INTO TKOF POS ON RWY 19 -- WE BOTH HEARD OVER THE SPEAKER THE SOUND OF SOMEONE KEYING THEIR XMITTER 3 TIMES. NEITHER OF US SAID ANYTHING TO EACH OTHER BUT WE BOTH DEFINITELY HEARD IT. THE TURN ON TO RWY 19 WAS A 180 DEG TURN TO THE R SO I HAD AN EXCELLENT VIEW TO SEE IF THERE WERE ANY VISUAL SIGNS OF AN ACFT LINED UP ON FINAL; ABOUT TO LAND. SEEING AND ALSO HEARING NOTHING ON THE ADVISORY FREQ (OTHER THAN THOSE 3 CLICKS); THE 'RWY ITEMS' WERE COMPLETED AND I HEARD MY FO ANNOUNCE TO BOTH FACILITIES (MENTIONED EARLIER); THAT 'FLT WAS NOW DEPARTING RWY 19 AT BREMERTON.' THE TKOF AND INITIAL CLB WAS INTO WHAT I WOULD JUDGE TO BE A MOSTLY BROKEN TO OVCST LAYER OF STRATUS CLOUDS AT BTWN 500 FT AND 600 FT AGL. IT WAS A THIN LAYER (NOT MUCH MORE THAN 100 FT). WE BROKE OUT AT WHAT I RECALL TO BE ABOUT 800-1000 FT AND JUST AS I WAS CALLING FOR 'FLAPS UP' AND MY FO WAS CALLING SEATTLE TO INFORM THEM THAT WE WERE AIRBORNE; THE UNMISTAKABLE PATTERN OF THE POS LIGHTS OF ANOTHER ACFT APPEARED OFF TO MY L SIDE AT AN ALT ABOVE OURS. IMMEDIATELY; I COULD TELL EASILY THAT THE ACFT WAS CLOSE AS I COULD DISTINCTLY SEE EACH ONE OF ITS 3 PRIMARY POS LIGHTS. WHAT WAS NOT SO EASY TO FIGURE OUT WAS THE ACFT'S FLT PATH RELATIVE TO OURS AND WHAT THE NECESSARY CTL INPUT WOULD BE REQUIRED TO AVOID A COLLISION. MY FIRST ACTION WAS TO BANK SLIGHTLY TO THE L AND STOP THE CLB. I DID THIS WHILE MY FO WAS TALKING TO SEATTLE; TELLING THEM THAT WE WERE AIRBORNE AND CLBING TO 5000 FT. IT WAS AT THIS MOMENT THAT MY FO CAUGHT A GLIMPSE OF THIS OTHER ACFT; AND HEARD ME SAY SOMETHING LIKE; 'WE'VE GOT CLOSE IN TFC HERE.' THERE WAS REALLY NO TIME FOR ANY ANALYTICAL THOUGHT HERE; MY INSTINCT WAS TO AVOID HITTING THIS ACFT BY KEEPING IT IN SIGHT; THEREFORE BEING ABLE TO MANEUVER MORE EFFECTIVELY FOR COLLISION AVOIDANCE. WITH OUR WINGS LEVEL AND RATE OF CLB NEAR ZERO; THE AIRPLANE APPEARED TO PASS BELOW OUR ALT BUT IT REMAINED ON OUR L SIDE. MY LAST VIEW OF THE ACFT WAS BELOW AND TO THE L. IT APPEARED TO BE HEADING IN ABOUT THE SAME DIRECTION AS WE WERE; AND MOVING SOMEWHAT SLOWER THAN OUR 200-220 KTS. ITS POS LIGHTS; I SAW AS DID MY FO. THERE MIGHT HAVE BEEN A FLASHING BEACON VISIBLE AND WE BOTH AGREE THAT THERE WERE NO FLASHING STROBES THAT EITHER OF US COULD SEE. AS TO HOW CLOSE THE AIRFRAMES OF OURS AND THIS OTHER ACFT'S CAME TO EACH OTHER; IS DIFFICULT TO SAY EXACTLY; MY BEST GUESS WOULD BE A FIGURE OF ABOUT 200 YDS; MAYBE 100 YDS. AS WE CONTINUED ON OUR WAY; THERE WAS NOMENTION OF ANY TFC; CLOSE IN OR OTHERWISE BY SEATTLE AND THERE WERE NO COMMENTS ON 122.7; WHICH MY FO AT THAT TIME CHKED AND VERIFIED WE WERE STILL MONITORING. THE TIME INTERVAL BTWN THE FIRST SIGHTING AND LAST GLIMPSE WAS SHORT; 10-15 SECONDS MAX. THIS INCIDENT TOOK PLACE WHILE TRANSITING CLASS E AIRSPACE ON AN INST CLRNC. THE OTHER ACFT WAS ALMOST CERTAINLY FLYING UNDER VISUAL FLT RULES. AS TO WHETHER THOSE 3 'CLICKS' XMITTED ON 122.7 SHORTLY BEFORE OUR DEP CAME FROM THE ACFT THAT WE BOTH SAW IS UNKNOWN. DURING THE REST OF THE TRIP TO LOS ANGELES; THERE WERE NO XMISSIONS MADE BY EITHER ATC OR THE FLC OF FLT XX REGARDING THIS INCIDENT.