A DSNDING B737-300 IN CLASS B AIRSPACE N OF PHX HAS AN NMAC WITH XING TFC THAT APPARENTLY HAD NO XPONDER IN OP.

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NMAC. WE WERE ON THE FOSSEL 4 ARR INTO PHX AND HAD PASSED TONTO (PXR 015 DEG RADIAL 34 DME) AND BEEN CLRED TO 8000 FT; TO SLOW TO 210 KTS AT 10000 FT. WE WERE GIVEN A HDG OF 170 DEGS AND HAD SLOWED TO 210 KTS AND STARTED OUR DSCNT OUT OF 10000 FT. SHORTLY AFTER I (CAPT) SAW AN ACFT AT OUR 1:30 O'CLOCK POS AND POINTED IT OUT TO THE FO WHO WAS FLYING. HE SAW THE ACFT AND ACKNOWLEDGED. THE ACFT AT FIRST APPEARED TO BE A B737 OR AN A320 (CLBING OR LEVEL AROUND 8000 FT) COMING OUT OF PHOENIX. THE ACFT APPEARED TO BE ABOUT 1000 FT BELOW AND COULD HAVE BEEN LEVEL OR IN A SLIGHT CLB. BUT ALMOST IMMEDIATELY I RECOGNIZED IT AS A MUCH SMALLER ACFT (SOME TYPE OF LIGHT TWIN; POSSIBLY TURBOPROP) AND IT NOW APPEARED ABOUT 500 FT BELOW. THE FO WAS FLYING AND I MOVED MY HANDS TO THE CTLS IN ORDER TO TAKE CTL IF NECESSARY. THE OTHER ACFT PASSED AROUND 300 FT BELOW US. AT NO TIME DID I FEEL LIKE HE WOULD HIT US. HOWEVER; HE DID PASS CLOSER THAN I BELIEVED HE WOULD INITIALLY. MY GUESS IS THE OTHER ACFT WAS ABOUT 1 MI AWAY WHEN WE FIRST SAW HIM AND THE TOTAL TIME LESS THAN 10 SECONDS. AFTER HE PASSED; WE CALLED APCH AND TOLD HIM OF THE NEAR MISS. HE (THE CTLR) SAID HE HAD A BLIND SPOT ABOUT THERE AND THEN ALMOST IMMEDIATELY SAID HE HAD A PRIMARY TARGET 3 MI BEHIND US. HE ASKED US INFO ON THE ALT OF THE OTHER ACFT; TYPE ACFT AND ALT BTWN US (OF THE MISS). THE CTLR DID NOT HAVE AN IFR SQUAWK AND WAS NOT TALKING TO THE ACFT. THERE WAS NO TCASII RA'S OR WARNINGS FROM THE TCASII. ALL EXTERIOR LIGHTS WERE ON INCLUDING OUTBOARD LNDG LIGHTS. THERE WAS NO EVASIVE ACTION FROM THE OTHER ACFT AND NO INDICATION THAT HE SAW US. PREVENTIVE ACTION: CONTINUE TO EMPHASIZE VISUAL LOOKOUT -- WHY THIS ACFT WAS WHERE HE WAS AND NO ONE KNEW IT SHOULD BE OF CONCERN TO US ALL; BUT I'M SURE IT WILL HAPPEN AGAIN. HAD I HAD TO REACT; IT PROBABLY WOULD HAVE BEEN FAIRLY VIOLENT AND I AM AFRAID ONE OR MORE OF THE FLT ATTENDANTS (WHO WOULD HAVE BEEN UP MOVING THROUGH THE AISLES) MAY HAVE BEEN HURT (OR POSSIBLY SMALL CHILDREN) (SEATBELT SIGNS WERE ON). CONTRIBUTING FACTORS: TIME OF DAY (DUSK) AND REDUCED VISIBILITY/PERCEPTION. POS OF ACFT AND ALT WAS VERY SIMILAR TO OUR DEPS FROM PHX; IE; LARGER ACR ACFT ON NORMAL DEP. OUR OWN DSCNT (APPROX 1000 FPM) AND POSSIBLE INITIAL IMPRESSION THAT THE OTHER ACFT WAS LEVEL; VERY SHORT TIME LEFT AFTER REALIZING THE OTHER ACFT WAS SMALLER AND CLOSER THAN INITIALLY THOUGHT.