B737-700 WITH MCI AT FL410 EXPERIENCED TCAS RA WITH OPPOSITE DIRECTION TFC REQUIRING EVASIVE TURN TO AVOID.

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WE WERE LEVEL AT FL410 APPROX 225 MI SW OF IRK WHEN WE RECEIVED AN RA ADVISING US OF TFC ALSO AT FL410 (WRONG DIRECTION) IN OUR 1-2 O'CLOCK POS MOVING IN THE OPPOSITE DIRECTION. OUR TCAS SAID 'TFC; TFC; CLB; CLB' AS THE FO AND I ATTEMPTED TO VISUALLY ACQUIRE THE OTHER ACFT OUTSIDE. HOWEVER; WE WERE ALREADY AT OUR MAX ALT CEILING AND WE HAD IDENTED THE ACFT ON THE TCAS AND BY THAT TIME I WAS ROLLING INTO A 20-30 DEG BANKED L TURN AND THE OTHER ACFT WAS PASSING OFF OF OUR R SIDE. I'M NOT SURE OF THE LATERAL DISTANCE BTWN OURSELVES AND THE OTHER PLANE BECAUSE IT ALL HAPPENED VERY SUDDENLY; BUT IT SEEMED VERY CLOSE. THE FO NOTIFIED ATC OF OUR TURN TO THE L AND THE FACT THAT WE HAD JUST GOTTEN AN RA. THE CTLR RESPONDED BY TELLING US TO TURN 30 DEGS TO THE L; WHICH I WAS ALREADY IN THE PROCESS OF DOING BY THAT POINT. WE NEVER HAD ANY INFO FROM THE CTLR ABOUT AN ACFT AT OUR ALT PRIOR TO THE RA. OBVIOUSLY THIS WAS A CASE OF HUMAN ERROR AND LUCKILY OUR TCAS ALERTED US TO A POTENTIAL DISASTER ALTHOUGH NOT QUITE AS EARLY AS WE WOULD HAVE LIKED. A CONTRIBUTING FACTOR WOULD HAVE TO BE THE FACT THAT THE OTHER ACFT WAS AT AN ALT THAT IS VERY WRONG FOR HIS DIRECTION OF FLT. WX AND TFC VOLUME DID NOT SEEM TO BE FACTORS BECAUSE IT WAS A VERY CLR NIGHT AND SEEMED TO BE RATHER QUIET WITHOUT A LOT OF TFC.