LEARJET ON IFR TWR ENRTE CLRNC FROM GKY TO DAL HAS NMAC WITH A SAAB COMMUTER OPPOSITE DIRECTION.

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DEPARTED GKY APPROX XA55; PICKED UP IFR TWR-TO-TWR ABOUT 2000 FT MSL TO DAL. I ASKED THE CTLR (ALT WAS NOT SPECIFIED IN CLRNC -- ONLY HDG AND SQUAWK) WHAT ALT I COULD HAVE. HE REPLIED 'ANYTHING TO 4000 FT.' I REPLIED 'I'D LIKE 4000 FT' (EASIER TO SPOT DAL) AND WAS TOLD TO MAINTAIN 4000 FT. IN LESS THAN 4 MINS WE SPOTTED DAL; AND THE CTLR CLRED US FOR THE VISUAL; THEN SWITCHED US TO DAL TWR. WE HAD NOT YET BEGUN OUR DSCNT WHEN TWR CALLED TFC 12 O'CLOCK. IT WAS VFR; BUT NEITHER OF US HAD PREVIOUSLY SEEN THE TFC. THE MOMENT HE CALLED THE TFC WE INSTANTLY SPOTTED A SAAB COMMUTER IN A HARD L TURN. I ACKNOWLEDGED TO ATC AT THAT MOMENT THAT WE HAD THE TFC (30-45 DEG BANK) AND I ABRUPTLY NOSED OVER AND TURNED L. WE WERE SO CLOSE THAT OUR RECOGNITION LIGHT ILLUMINATED THE UNDERSIDE OF THE SAAB. WE MISSED EACH OTHER BY ABOUT 200 FT VERTLY AND HAD WE STILL BEEN AT 4000 FT; WOULD HAVE IMPACTED HORIZLY. I DON'T RECALL ANY FURTHER MENTION OF THE TFC/INCIDENT WITH ATC. WE PROCEEDED TO LAND. ONCE ON THE GND; I CALLED THE TWR AND ASKED TO SPEAK TO THE CTLR WHO HANDLED US. HE INFORMED ME THAT HIS AIRSPACE ONLY WENT UP TO 2000 FT MSL AND THE SAAB WAS BEING CTLED BY DFW APCH/DEP; AND APPARENTLY 'GOT AWAY' FROM THEM. SO I SURMISED I WAS IN DFW APCH'S AIRSPACE WHEN THE INCIDENT OCCURRED BUT WAS BEING WORKED BY TWR. THE TWR CTLR WAS SOMEHOW INSPIRED AT THAT MOMENT TO CALL TFC FOR US. HAD HE NOT; IT COULD HAVE BEEN WORSE. I HAVE A CONSIDERABLE AMOUNT OF TIME FLYING IN DFW AIRSPACE -- DAL; DFW; GKY; ADS -- PERHAPS 500 HRS IN THE DALLAS AREA ALONE; ALL IN LEARJETS AS PIC. I DON'T UNDERSTAND HOW THAT SAAB GOT SO CLOSE WITHOUT US SEEING HIM; UNLESS HE WAS CLBING DIRECTLY AT US AND VISUALLY APPEARED AS A STATIONARY OBJECT. WHEN I CALLED THE TWR ON THE PHONE; HE WAS SURPRISED WE HADN'T SPOTTED THE TFC PRIOR TO HIS CALL. WE WERE SHOWING A RECOGNITION LIGHT (VERY BRIGHT LIGHT IN THE R WINGTIP) THROUGHOUT THE ENTIRE LEG; WHICH ONLY LASTED 6-7 MINS. BOTH MYSELF AND MY SIC WERE WELL RESTED AND ALERT; VIGILANT AND EXPERIENCED IN LEARJET OPS. MY ONLY SUGGESTIONS ON HOW OTHERS COULD PREVENT THIS TYPE OF OCCURRENCE IS TO BE EVEN MORE VIGILANT. I'M NOT ABOUT TO LAY THE BLAME ON SOME ANONYMOUS CTLR OR ACCUSE SOMEONE OF LAYING OUT AIRSPACE IMPROPERLY -- I DO BELIEVE THE BUCK STOPS HERE. I AM THANKFUL OUR TWR CTLR POINTED HIM OUT EVEN THOUGH HE WAS NOT (AND NEITHER WERE WE; THOUGH WE NOW BELONGED TO TWR) IN TWR'S AIRSPACE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR SAID HE WAS FLYING LJ25 AT 4000 FT FOR ABOUT 2 MINS AND THEN SWITCHED TO THE DAL TWR. HE SAID HIS ACFT IS NOT EQUIPPED WITH A TCASII SYS. HE ALSO SAID HE WAS ABOUT 5 MI SW OF DAL; HEAD-ON A COLLISION COURSE WITH THE OTHER ACFT.