POTENTIAL CONFLICT. LTT IN ALTDEV ALT EXCURSION. OPPOSITE DIRECTION CLBING TFC.

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WE WERE ON A PART 91 FLT TO OUR DEST. THE PURPOSE OF OUR FLT WAS A RETURN TRIP AFTER SUCCESSFULLY PASSING A FAR 135.297; 135.299 FLT CHK WITH AN FAA INSPECTOR. I WAS FLYING AS FO ON THIS LEG OF OUR FLT. OUR ACFT WAS CLRED DIRECT TO OUR DEST AND TO CLB AND MAINTAIN FL220. WHEN APCHING THE DEST AREA WE ASKED FOR LOWER ALT. THE CTR CTLR ADVISED US TO TURN L TO 250 DEGS AND MAINTAIN FL220. THE CTLR ADDITIONALLY RPTED OPPOSITE DIRECTION TFC THAT I RPTED WE HAD IN SIGHT. THE FOLLOWING EVENTS TOOK PLACE NEXT. I BEGAN RUNNING THE DSCNT CHKLIST; AND WAS PROCEEDING TO SET UP THE ACFT FOR THE INST APCH TO OUR DEST. AS I LOOKED UP TO THE FLT INSTS I NOTICED OUR ACFT WAS DSNDING FROM FL220 WITH FL200 SET INTO THE ALT SELECT. I ASKED THE CAPT IF WE WERE CLRED TO FL200 AND THE CAPT REPLIED YES. OUR ACFT HAD THE TFC ON TCASII AND WE ALSO HAD VISUAL CONTACT WITH THE TFC. THE CTLR ASKED US WHAT ALT WE WERE AT; AND I REPLIED LEVEL AT FL200. AFTER CLRING THE TFC; WE WERE INSTRUCTED TO TURN R ON COURSE AND ISSUED A DSCNT CLRNC TO 14000 FT; OUR ACFT LANDED AND WE IMMEDIATELY TELEPHONED THE CTR ATC MGR TO DISCUSS THE SIT. I BELIEVE THAT SEVERAL FACTORS WERE INVOLVED WITH THIS SIT THAT INCLUDED A BREAKDOWN OF CRM. WE; AS A CREW; WERE VERY FATIGUED AFTER COMPLETING 2 SEPARATE CHKRIDES IN ACTUAL WX CONDITIONS THAT INCLUDED SOME 9 ACTUAL IFR/IMC APCHS. OUR CREW WAS BY NO MEANS UNSAFE; BUT SIMPLY TIRED. THE LESSON OUR CREW LEARNED REAFFIRMS THE NECESSITY FOR CRM AND TO CONFIRM CRITICAL INSTRUCTIONS SUCH AS ALTS AND HDGS; ETC. SUPPLEMENTAL INFO FROM ACN 359233: DEPARTING FOR THE RETURN FLT HOME; THE FLC RECEIVED AN IFR CLRNC: DIRECT (310 DEGS); CLB AND MAINTAIN FL220. THE WX WAS CLR (50 NM) ABOVE THE FOG LAYER. ETE WAS 30 MINS. AT 40 NM TO DEST ARPT; THE FLC REALIZED THAT WE HAD NOT BEEN HANDED OFF TO ZOA (THE ARTCC FOR THE AREA). AFTER CONTACT WITH ATC WAS FINALLY ESTABLISHED; THE PNF REQUESTED A LOWER ALT FOR THE DSCNT. THE ACFT WAS STILL LEVEL AT FL220 AND NOW ONLY 25 NM FROM THE DEST ARPT. ATC APOLOGIZED FOR THE DISCREPANCY AND ISSUED A DELAY VECTOR; L TURN 250 DEGS; AND IN MY (THE PF) OPINION; HEARD A DSCNT CLRNC TO AND MAINTAIN FL200. THE DSCNT AND VECTOR BY ATC PLACED THE ACFT INTO ONCOMING TFC (B737) CLBING THROUGH FL200.