NMAC DURING THE INITIAL DEP PHASE OF AN IFR FLT FROM AN UNCTLED ARPT.

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WE EXPERIENCED AN NMAC IN VICINITY OF TYQ ARPT WHILE ON INITIAL CLBOUT IN THE TFC PATTERN. WE DEPARTED RWY 18 AT XA06Z. WE CALLED IND APCH PRIOR TO DEP. NO RECEIVING A VOID TIME CLRNC FOR THE TRIP; WHICH INCLUDED AN INITIAL CLB TO 3000 FT AND A VOID TIME OF XA10Z. FO OCCUPIED THE L SEAT AND WAS PF FOR THE TRIP. I OCCUPIED THE R SEAT AND WAS PNF. WX CONDITIONS AT THE TIME OF DEP WERE ESSENTIALLY CAVU WITH SURFACE WINDS FROM APPROX 240 DREGS AT 11 KTS GUSTING TO 17 KTS. PRIOR TO DEP; I MADE THE FOLLOWING CALLS ON THE TYQ CTAF: PRIOR TO TAXIING ONTO RWY 18; DURING BACK-TAXI OPS ON RWY 18; AFTER LIFTOFF DURING INITIAL CLBOUT WHILE STILL OVER THE RWY. EACH OF THESE CALLS INCLUDED OUR TAIL NUMBER; THE RWY WE WERE USING (RWY 18); THE DIRECTION OF TURNS WE INTENDED TO MAKE IN THE TFC PATTERN (L); THE ALT WE WOULD BE CLBING TO 3000 FT; AND OUR DIRECTION FO DEP (NBOUND). EACH CALL ENDED WITH A REQUEST THAT ANY TFC IN THE AREA ADVISE THEIR POS. FO CLBED STRAIGHT AHEAD TO 500 FT AGL AND INITIATED A L TURN TO THE XWIND LEG. AT FO'S CALL; I PERFORMED A PWR REDUCTION TO CLB PWR DURING THE TURN. WHEN WE WERE ESTABLISHED ON A L XWIND; ANOTHER ACFT RPTED ITS POS ON TYQ CTAF AS 4 MI E OF THE ARPT AT AN ALT BELOW US; THAT THEY WERE CONDUCTING AN INSPECTION OF REAL ESTATE. I MADE ANOTHER CTAF CALL TO RESPOND; THIS TIME RPTING OUR POS (TURNING DOWNWIND); CURRENT ALT (2700 FT); CLBING TO 3000 FT; INTENDING TO DEPART THE AREA NBOUND. I GLANCED AT MY WATCH AND NOTICED THE TIME WAS APPROX XA08. THOUGH NOT YET OUT OF THE ARPT VICINITY; I WAS ANXIOUS TO ESTABLISH CONTACT WITH IND DEP PRIOR TO XA10; SO THEN SWITCHED FREQS AND MADE OUR INITIAL CALL-UP WITH IND DEP. AT THIS POINT; FO SPOTTED THE OTHER ACFT AND LEVELED THE WINGS. WE WERE ON AN APPROX NE HDG IN THE TURN. I LOOKED UP AND SAW THE OTHER ACFT JUST AHEAD OF US AT MY 11:30 POS; IN A VERT BANK; DSNDING; THE NOSE OF THE ACFT ORIENTED NW SO THAT WE COULD PLAINLY SEE THE BELLY OF THE ACFT (APPEARED TO BE A DECATHLON). JUDGING FROM THE SIZE OF THE ACFT IN THE WINDSHIELD; IT APPEARED TO BE MUCH LESS THAN 500 FT FROM OUR POS (PERHAPS AS LITTLE AS 200 FT). FO BEGAN AN ASCENDING R TURN AWAY FROM THE ACFT; WHICH NOW APPEARED TO HAVE ROLLED PAST VERT AND WAS RAPIDLY DSNDING BELOW OUR FLT PATH. THERE WAS SOME CONFUSION AS WE LOST SIGHT OF THE ACFT BELOW US. IND DEP RESPONDED TO OUR INITIAL CALL-UP AND RPTED TFC AT OUR POS; ALT UNKNOWN. THE CTLR ALSO APPARENTLY GAVE US RTE OF FLT AND CLB INSTRUCTIONS. I RESPONDED THAT WE HAD SEEN THE TFC. WE CONTINUED TO LOOK FOR THE OTHER ACFT. FO COMPLETED THE TURN TO A NBOUND HDG AND LEVELED THE ACFT AT 3000 FT. BOTH OF US FINALLY SPOTTED THE OTHER ACFT WELL BELOW US AT OUR 10 O'CLOCK POS; HDG EBOUND. IT APPEARED TO BE FLYING NEAR GND LEVEL. WE DID NOT RPT THE NMAC TO THE CTLR AND MADE NO FURTHER CALLS ON TYQ CTAF. MY JUDGEMENT IS THAT THIS WAS IMPROPER. SOME OBSERVATIONS ON THIS POINT: AT THE TIME OF THE INCIDENT; I DID NOT QUESTION IF THE ACFT WE SPOTTED WAS THE ACFT THAT MADE THE CTAF CALL. I ASSUMED THAT IT WAS; AND THUS THAT IT WAS INVOLVED IN A NECESSARY EVASIVE MANEUVER. HAD I SUSPECTED THAT THE ACFT MAY HAVE IN FACT BEEN SOME OTHER TFC INVOLVED IN INTENTIONAL AEROBATIC MANEUVERS IN OR NEAR THE TFC PATTERN OF THE ARPT; I WOULD CERTAINLY HAVE MADE A RPT TO ATC. SINCE THE INCIDENT OCCURRED AT THE MOMENT THAT WE WERE BOTH IN A VFR TFC PATTERN; AND MAKING OUR INITIAL CALL-UP TO IND DEP; I ALSO DID NOT JUDGE THAT THERE WAS ANY FAILURE ON THE CTLR'S PART TO RPT A TFC CONFLICT TO US. HAD WE ALREADY BEEN INFORMED THAT WE WERE IN RADAR CONTACT; I WOULD HAVE RPTED THE CONFLICT TO THE CTLR IMMEDIATELY. GIVEN THE TIMING OF THE EVENT AND OUR PHASE OF FLT; I THOUGHT IT BEST TO STAY FOCUSED ON THE TASKS OF OUR FLT. WE BOTH EXPERIENCED A MOMENT OF SHOCK OVER THE INCIDENT AND IT WAS CLR TO ME IMMEDIATELY THAT WE NEEDED TO FORCE OURSELVES BACK INTO THE GAME; REGAIN OUR COMPOSURE AND STAY FOCUSED ON WHAT WE NEEDED TO DO FROM THAT POINT FORWARD. WE REQUESTED CLARIFICATION FROM THE DEP CTLR OF OUR COURSE AND ALT CLRNCS; AND I URGED FO TO STAY FOCUSED ON OUR FLT IN SPITE OF HOW HE MIGHT HAVE FELT AT THAT MOMENT. I HAD FLOWN 5 OF THE LAST 7 DAYS (INCLUDING DAY OF INCIDENT); 19 LEGS; 31 HRS FLT TIME. I WAS FATIGUED. DUE TO MY OWN MISINTERP OF CLRNC VOID TIME IN A VOID-TIME CLRNC; WAS DISTR WITH CONCERN OF MAKING DEP CALL-UP AND THUS WAS NOT PROPERLY VIGILANT IN THE TFC PATTERN. I DID NOT NEED TO WORRY ABOUT THIS RADIO CALL AND SHOULD HAVE INSTEAD BEEN MAXIMALLY VIGILANT. OPS FROM AN UNCTLED ARPT INTO THE IFR ENVIRONMENT REQUIRE EXTRA VIGILANCE AND CAUTION TO AVOID UNNECESSARY DISTR AND CONFUSION.