LEAR 45XR FLT CREW HAS AN ALT EXCURSION DURING LEVELOFF AT CRUISE ALT.

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WE WERE CLBING OUT SAT ON THE ALAMO 6 SID AND IN THE VICINITY OF SEEDS INTXN WE WERE GIVEN DIRECT TO LFK VOR AND AN INTERIM LEVELOFF OF FL390 FOR OPPOSITE DIRECTION TFC AT FL400. WE WERE SOMEWHERE SW OF BRENHAM AS OUR ALT APCHED FL390 WITH THE AUTOPLT ON AND THE FLT LEVEL CHANGE MODE ENGAGED. THE AUTOPLT ALT WINDOW WAS SET FOR FL390. IMMEDIATELY PRIOR TO ME WATCHING FOR ALT CAPTURE BY THE AUTOMATIC FLT CTL SYS; ZHU CALLED OUT THE OPPOSITE DIRECTION TFC TO US WHICH WE HAD BEEN LOOKING AT ON TCAS. WE HAD AN EASY VISUAL SIGHTING OF THE OTHER JET. THE MORNING WAS SO CLR THAT IT WAS HARD NOT TO WATCH THE CONTRAILS OF IT EVEN THOUGH IT WAS NEARLY 20 MI AWAY. ANYWAY; AFTER STARING AT THE TFC A FEW SECONDS TOO LONG; I LOOKED AT OUR ALT AND SAW THAT WE WERE FL391 AND CLBING. I HIT THE AFCS VERT SPD MODE AND DIALED IN A DSCNT. OUR INERTIA CARRIED US UP TOWARDS FL393. I DISCONNECTED THE AUTOPLT AND FLEW THE ACFT BACK DOWN. THE ALT ALERTER CHIME SOUNDED (300 FT) AND OUR TCAS ADVISORY GAVE US 'TFC; TFC.' AS WE WERE DSNDING; ZHU ASKED US ABOUT OUR ALT. WE TOLD HIM WE WERE LEVELING AT FL390. WHEN WE GOT TO FL390; ZHU ASKED US TO CONFIRM THAT WE WERE AT FL390. WE CONFIRMED IT AND ABOUT 20 SECONDS LATER WE WERE ABEAM THE TFC. I'M SURE THE OTHER ACFT GOT A TCAS ADVISORY. OUR MAX ALT REACHED FL393. I ANTICIPATE AND WATCH FOR ALT CAPTURE WHEN USING THE AFCS. IT HAS ALWAYS CAPTURED ALT WHEN IT WAS ARMED. I WAS DISTR BY WATCHING THE ACFT I WAS SUPPOSED TO AVOID GETTING CLOSER TO THAN 1000 FT VERTLY; AND THE ACFS DID NOT CAPTURE THE ALT.