WITH DFW TWR PROVIDING VISUAL SEPARATION TO 2 ACRS A TCASII RA WAS FLOWN BY ONE AND AN ABRUPT DIVE MADE BY THE OTHER AT LOW ALT TO AVOID CONFLICT.

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I WAS FLYING AS FO ON A B727 DEPARTING RWY 36R AT DFW. CLRED FOR TKOF AND ASSIGNED 345 DEG HDG. AT THE DEP END OF THE RWY WE TURNED TO 345 DEGS AND AT 800 FT AGL WE DECREASED OUR CLB RATE TO 500-1000 FPM AND BEGAN TO RAISE THE FLAPS. WE HAD NOT COMPLETED RECONFIGURING WHEN WE PASSED THROUGH 1100 FT AGL AND IMMEDIATELY GOT A CLB RA. (TCASII RA'S ENABLE AT 1100 FT AGL.) THE CAPT QUICKLY INCREASED OUR CLB BUT WE HAD TO USE CARE AS WE WERE AT OR SLIGHTLY BELOW MANEUVERING SPD. I BEGAN A VISUAL LOOKOUT FOR THE ACFT AND SAW NOTHING. THEN CHKING THE TCASII I SAW A RED TARGET DEAD CTR AT -01. THE TARGET BEGAN TO DSND AND WE GOT A 'CLR OF CONFLICT' AURAL SIGNAL. WE ASKED DEP FOR A TWR PHONE NUMBER AND CALLED AFTER THE FLT. WE WERE TOLD THE OTHER ACFT WAS A SAAB 340 THAT HAD DEPARTED RWY 36L AT A MID-FIELD INTXN. WE WERE NOT ADVISED OF THE SAAB. I AM NOT SURE WHETHER OR NOT HE WAS ADVISED OF US. HE WAS ASSIGNED A DEP HEADING OF 270 DEGS. THE TWR SUPVR SAID HE WAS PROVIDING VISUAL SEPARATION AND HAD BOTH ACFT IN SIGHT. HE TOLD US THE SAAB MADE AN ABRUPT DSCNT APPARENTLY IN RESPONSE TO OUR CLOSE PASS. I DON'T KNOW IF THIS WAS DUE TO VISUAL CONTACT OR AN RA ON HIS PART AS WELL. IT WAS IMPOSSIBLE FOR US TO SEE THE SAAB AS OUR NOSE WAS AT LEAST 10-15 DEGS HIGH DURING TKOF AND THE INITIAL CLB. WHEN ASKED WHY THEY VECTORED US TOWARD THE ADJACENT RWY WHEN ACFT WERE TAKING OFF WE WERE TOLD THIS WAS TO AVOID THE RWY 35 DEPS AND WAS STANDARD. WE NEVER SAW THE SAAB; BUT BELIEVE WE CAME VERY CLOSE (100-200 FT) IN A VERY CRITICAL PHASE OF FLT. NORMALLY; ACCORDING TO THE TWR SUPVR; WE WOULD BE ADVISED OF TFC DEPARTING ON ADJACENT RWYS. HAD THIS BEEN THE CASE; WE COULD HAVE MONITORED THE TFC; BEEN MORE CAUTIOUS OF HIS POS AND POSSIBLY AVOIDED THE CONFLICT. WE SHOULD NOT HAVE BEEN GIVEN A TURN TOWARDS THE TFC UNTIL HE WAS WELL ESTABLISHED ON HIS WESTERLY HEADING.