WBOUND B737 HAD NMAC SHORTLY AFTER DEPARTING MCI. FLT WAS CLBING THROUGH FL320 WHEN THE TCASII ORDERED A DSCNT.

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ACR X KANSAS CITY INTL TO DENVER INTL APR/XA/98 XA40. WHILE ENRTE FROM KANSAS CITY INTL (MCI) TO DENVER INTL (DIA) WE TOOK EVASIVE ACTIONS PER OUR TCASII RA TO DSND WHILE PASSING THROUGH FL321. AFTER DEPARTING MCI WE WERE INITIALLY CLRED TO FL280. NUMEROUS EBOUND ACFT ABOVE US PREVENTED THE CTLR FROM ASSIGNING A HIGHER ALT. AFTER CLRING ALL EBOUND TFC THE CTLR (ZKC) ISSUED US A CLRNC TO CLB TO FL350. THE WX WAS THIN CLOUDS PARTIALLY OBSCURING OUR FORWARD VISION. WHILE PASSING THROUGH FL321 I NOTICED TFC AT FL330 COMING AT US FROM THE SW (APPROX 10 O'CLOCK HIGH) DISPLAYED ON MY EHSI. THE TCASII IMMEDIATELY ORDERED A DSCNT. I WAS ABLE TO SEE THE ONCOMING TFC AS IT PASSED DIRECTLY OVER US. AT THE TIME OF THIS CONFLICT I ESTIMATE ABOUT 1000-1100 FT OF SEPARATION. I NOTIFIED ZKC AS SOON AS I RECEIVED THE TCASII ORDER TO DSND. THE APCHING ACFT ADVISED CTR OF THEIR TCASII ALERT SHORTLY AFTER MY XMISSION. AFTER WE WERE CLR OF THE CONFLICT I ADVISED THE CTR THAT WE WOULD CONTINUE CLBING TO OUR ASSIGNED ALT OF FL350.