OPERROR WHEN AN MD80 CLBED THROUGH THE ALT OF A DA20 WITH LTSS. TRAINEE ON POS. INSTRUCTOR'S ATTN MOMENTARILY AWAY FROM WATCHING AND LISTENING TO DOCUMENT PREVIOUS OJT DEFICIENCY. INSTRUCTOR ACTIONS TAKEN TOO LATE TO AVERT ERROR. MD80 RPTED TCASII RA DSCNT ON NEXT CTR FREQ.

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I WAS PROVIDING ON THE JOB TRAINING TO A PARTIAL RADAR CERTIFIED TRAINEE AT A HIGH DENSITY HIGH ALT SECTOR AT ZAU. THIS PARTICULAR TRAINEE HAD MANY PROBS AND WAS ON THE THIRD RECYCLE THROUGH RADAR AND SECOND AREA OF SPECIALIZATION AT ZAU. DURING A PERIOD OF LIGHT TO MODERATE TFC THE TRAINEE HAD 2 ACFT STOPPED AT FL250 (MD80/F AND B727/A) FOR A DA20/R. TRAINEE FAILED TO APPLY MERGING TARGET PROCS ON THE B727 AND THE DA20. ACFT PASSED LESS THAN 1 MI UNTIL ACFT WERE JUST PRIOR TO PASSING. AS I WAS DOCUMENTING THIS DEFICIENCY; THE TRAINEE THEN CLRED THE MD80 TO MAINTAIN FL330 AND DIRECT SUM THEN SWITCHED THE ACFT TO ZOB FREQ. I ATTEMPTED TO GET THE MD80 BEFORE THE ACFT LEFT FREQ BUT WAS UNSUCCESSFUL. THE MD80 AND DA20 WERE MERGING AND WERE ONLY APPROX 6 MI APART. THE MD80 STARTED TO CLB. INITIAL SEPARATION WAS LOST AS 3.7 MI AND 700 FT. PLT OF THE MD80 CHKED ONTO ZOB FREQ AND ADVISED THAT HE WAS EXECUTING A DSND 'RA.' THE MD80 THEN ADVISED THAT HE HAD MISSED AN ACFT BY ONLY 200 FT AND WAS GOING TO FILE A NEAR MISS RPT. THE PROB AROSE WHEN I IN FULFILLING MY DUTIES AS AN OJT INSTRUCTOR; MOMENTARILY TOOK MY ATTN FROM WATCHING AND LISTENING TO MY TRAINEE; IN ORDER TO DOCUMENT AN ERROR. DUE TO THE PROX OF THE CONFLICTING TFC AND THE FREQ CHANGE TO ZOB I WAS NOT ABLE TO CORRECT THE TRAINEE'S ERROR WHICH RESULTED IN THE MD80 TAKING EVASIVE ACTION. ATTEMPTS TO COORDINATE WITH ZOB WERE MADE; BUT AGAIN TIME WAS NOT AVAILABLE NOR WAS THE ACFT ON ZOB'S FREQ; BUT BTWN FREQS.