AN NMAC IS AVERTED BY TCASII AND TURNED INTO A POTENTIAL CONFLICT. A CLBING DEP MD80 DIVES TO AVOID A C172 AT THEIR ASSIGNED ALT OF 4000 FT.

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PSP DEP; 5 MI ESE OF PSP. AFTER DEPARTING RWY 13R AT PSP MY FO WAS FLYING A 100 DEG HDG AND CLBING TO 4000 FT IN ACCORDANCE WITH OUR CLRNC. THE TWR CTLR INSTRUCTED US TO CONTACT DEP CTL ON 126.7. THERE WERE NUMEROUS ACFT IN THE AREA AND BOTH CTLRS WERE VERY BUSY. AFTER TUNING IN THE DEP FREQ I HAD TO WAIT FOR SOME TIME BEFORE CALLING BECAUSE THE CTLR WAS BUSY GIVING INSTRUCTIONS TO OTHER ACFT INCLUDING WHAT SOUNDED LIKE A FULL RTE CLRNC TO AN ACFT ON THE GND. DURING THIS TIME I NOTICED A TARGET ON OUR TCASII IN ABOUT OUR 1:30 O'CLOCK POS AND ABOUT 4 MI WHICH APPEARED TO BE LEVEL AT 4000 FT. I ASKED THE FO TO SLOW HIS RATE OF CLB AND WE BOTH STARTED LOOKING FOR THE TFC. WE ACQUIRED HIM VISUALLY ALMOST IMMEDIATELY. HE APPEARED TO BE A CESSNA 172; LEVEL AT 4000 FT; AND ON ABOUT 080 DEG OR 090 DEG HDG. ABOUT THIS TIME WE WERE CLBING THROUGH ABOUT 3500 FT AND WE RECEIVED A TA FROM THE TCASII FOLLOWED IMMEDIATELY BY A DSND RA. MY COPLT DSNDED TO ABOUT 3100 FT BEFORE WE RECEIVED THE CLR OF CONFLICT RPT FROM THE TCASII. THE CESSNA PASSED ABOVE AND SLIGHTLY BEHIND US. IT APPEARED TO ME THAT AT ABOUT THE SAME TIME WE STARTED OUR DSCNT THE CESSNA ALSO PITCHED OVER. POSSIBLY HE THOUGHT WE WERE STILL CLBING AND WAS ATTEMPTING TO PASS BELOW US. IT IS HARD TO SAY WHETHER OUR TCASII PREVENTED A COLLISION BUT IT CERTAINLY KEPT A CLOSE ENCOUNTER.