ACR FLC INITIATE TCASII EVASIVE MANEUVER DUE TO SAME ALT XING TFC IN N90 AIRSPACE.

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ACFT HAD LEVELED OFF AT 6000 FT ON THE EWR DEP OUT OF EWR. DEP CTL CALLED B727 TFC; AT 7000 FT; FROM R TO L IN FRONT OF ACFT. I THEN SAW ANOTHER TARGET ON THE TCASII AT 6000 FT (CO-ALT) AT 2 O'CLOCK; 5 MI AND CLOSING. I ASKED DEP IF HE HAD THIS TFC. BEFORE HE COULD RESPOND; THE TCASII GAVE AN RA ALERT ALONG WITH 'CLB' COMMAND. THE FO WAS FLYING AND I DIRECTED HIM TO CLICK OFF THE AUTOPLT AND COMMENCE A SLOW CLB BECAUSE THE B727 TFC WAS PASSING IN FRONT OF US AT 7000 FT. WE CLBED TO 6300 FT; LEVELED OFF; AND SPOTTED THE 6000 FT TFC PASSING OUR R SIDE AT 1 1/2 MI. WE TOLD DEP WE WERE CLR OF TFC AND DSNDED BACK TO 6000 FT. WE PASSED UNDER THE B727 AT 7000 FT SHORTLY THEREAFTER. WE ASKED THE CTLR WHERE THE CO-ALT TFC HAD COME FROM AND HE REPLIED IT WAS WITH APCH CTL AND HE'D FIND OUT WHAT HAPPENED. THIS APPEARS TO BE A BREAKDOWN BTWN DEP AND APCH CTL. DEP SEEMED AS SURPRISED AS WE WERE WHEN THE TFC POPPED UP. WHAT REALLY MADE THE SIT DANGEROUS WAS THE B727 TFC AT 7000 FT ON OUR NOSE. IT WAS ALMOST LIKE BEING DRIVEN INTO A BOX CANYON. AS A CREW; WE KEPT TALKING TO EACH OTHER AND EVALUATING THE SIT AND OUR ACTIONS TO ENSURE SAFETY. WE HAVE HAD A LOT OF CRM TRAINING THE LAST SEVERAL YRS AND IT CAME IN HANDY. SUPPLEMENTAL INFO FROM ACN 430340: THE PURPOSE FOR WRITING THIS IS TO DETAIL A POSSIBLE FAILURE TO INTERCEPT A RADIAL ALONG FLT PLAN RTE AT A TURNPOINT RESULTING IN LOSS OF HORIZ SEPARATION BTWN OUR ACFT AND UNKNOWN OTHER(S). THE UNUSUAL AND MITIGATING CIRCUMSTANCES PROVIDE THE CAUSE FOR IT AND MAY BE HELPFUL IN PREVENTING FUTURE OCCURRENCES. BEGINNING WITH A SEEMINGLY NORMAL TKOF AT EWR ON RWY 22L; WE INCURRED A VERT GYRO FAILURE ON THE R (FO) SIDE WITH SIMULTANEOUS FAILURE OF BOTH DME'S (OR DME XMITTER ON THE FIELD). TKOF WAS ACCOMPLISHED BY ME WITHOUT ANY COCKPIT PRESENTATION OF PITCH OR BANK ASIDE FROM LOOKING OUT THE SIDE WINDOW AND LOOKING TO THE L SIDE CAPT'S VERT GYRO FOR REF. THE SID (EWR 6 DEP; WHITE TRANSITION) REQUIRES 5 TURNS UNTIL PROCEEDING ON COURSE. WE ATTEMPTED THE FIRST 2 WITHOUT DME; THEN SWITCHED TO FO ALTERNATE GYRO. A SHORT TIME LATER AT 5000 FT OR 6000 FT; OUR TCASII SHOWED A TFC CONFLICT AT 3 O'CLOCK; SAME ALT; COMING TOWARD US (EBOUND). WHILE WE WERE ON COURSE PROCEEDING SBOUND ON OR NEAR THE COLTS NECK 350 DEG RADIAL; THE TCASII THEN GAVE A 'CLB' COMMAND. WX WAS MVFR. I BEGAN A SLIGHT 200-300 FT CLB WHILE OBSERVING TFC PASSING OFF OUR R AND BEHIND US WITHIN 2 MI. THE CAPT (PNF) NOTIFIED NEW YORK DEP OF OUR TCASII TFC AND INFORMED THEM WE WERE CLBING. ATC ACKNOWLEDGED AND APOLOGETICALLY INDICATED IT WAS THEIR ARR TFC INTO EWR. THEY THEN ASKED US TO RETURN TO ASSIGNED ALT WHEN ABLE DUE TO PASSING TFC ABOVE; FROM R TO L (W TO E) ABOVE US 1000 FT. WE COMPLIED. THE COCKPIT IN ALL THIS WAS EXTREMELY BUSY WITH CREW COORD REGARDING COLLISION AVOIDANCE MANEUVER; MULTIPLE COCKPIT INST FAILURE EARLIER; AND CONTINUING REAL TIME TFC OBSERVANCE IN THE VICINITY. SOMEWHERE AND SOMETIME SHORTLY AFTERWARDS; WE MAY HAVE OVERFLOWN A TURNPOINT AT WHITE INTXN TO INTERCEPT THE COYLE 226 DEG COURSE. ATC BY NOW HAD BEEN SWITCHED; WE THINK; TO ZNY OR ZDC; WHO WAS LIKELY UNAWARE OF OUR TCASII CONFLICT AND RESULTING DEV FROM FLT PATH. THIS COULD ONLY BE PREVENTED IN FUTURE BY THOROUGH COM BTWN ATC FACILITIES OR QUICKER PLT REACTION TO COURSE TRACKING WHILE IN THE MIDST (OR SHORTLY AFTER) OF AN EMER MANEUVER SIT. ALSO; IT WOULD HELP IF ATC WOULD CALL OR WARN ACFT IF THEY SENSE A POTENTIAL CONFLICT.