MD80 CREW HAD A NMAC WITH A LIGHT ACFT IN OMA CLASS C; AFTER THE LIGHT ACFT PLT WAS NOT ABLE TO MAINTAIN HIS ASSIGNED ALT.

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ARRIVING FROM THE E INTO OMA; WE HEARD SEVERAL CALLS TO A LIGHT ACFT REGARDING HIS VARIATIONS IN ALT. THERE WERE 3 ACFT ON OUR TCASII; 1 AT 11 O'CLOCK POS AND 2 AT 2 O'CLOCK POS. 2 ACFT WERE AT 4000 FT; AND 1 WAS ABOVE OUR ALT -- I THINK. ALL ACFT WERE ABOUT 5 MI AWAY WHEN WE FIRST COMMENTED ON THE TFC IN FRONT OF US; AND APCH GAVE US A SLIGHT VECTOR AWAY FROM THE 11 O'CLOCK TFC. HE WAS SUPPOSED TO BE AT 3500 FT; BUT TCASII SHOWED HIM AT 3800-4000 FT. AT 2 MI; I COMMENTED THAT THIS WAS GOING TO BE CLOSE AND TOLD THE CAPT I WAS TURNING FURTHER R TO AVOID THE TFC. SOON AFTER; WE RECEIVED THE TA AND ALMOST IMMEDIATELY; RECEIVED THE RA. I CLBED PER THE RA INSTRUCTIONS AND TURNED AWAY FROM THE LOCATION OF THE TARGET. THE LAST TIME I LOOKED AT THE TCASII; HIS TARGET HAD MERGED WITH OUR AIRPLANE SYMBOL ON THE VSI; AND IT SHOWED 200 FT BELOW US. WE RPTED THE RA TO APCH AND THEN CONTACTED THEM UPON ARR. APCH SAID HE NEVER GOT WITHIN 400 FT; BUT I KNOW WHAT I SAW. WE NEVER VISUALLY ACQUIRED THE TARGET DUE TO HAZY -- SUNSET CONDITIONS.