DISPATCHED WITH A DEFERRED ALT ALERT SYSTEM; SF340 FLT CREW SUFFERS ALT DEV ON RAPID DESCENT TO 10000 FT REQUIRED DUE TO A FAILURE OF BOTH ENG BLEEDS.

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WHEN WE ARRIVED AT THE ARPT; I LOOKED AT THE RELEASE AND SAW THE DEFERRAL FOR THE FLT DECK ALT ALERTING SYS. I BRIEFED THE FO ON THIS AND WE REVIEWED THE FLT CREW ACTIONS LISTED IN THE MEL. HE WAS THE PF SO I WANTED TO BE SURE WE WERE BOTH IN AGREEMENT ON HOW THIS DEFERRAL WOULD AFFECT THE FLT OP. AT APPROX 11000 FT CLBING OUT; WE RECEIVED A MASTER CAUTION L BLEED FAULT AND L BLEED CLOSED ANNUNCIATOR LIGHTS. I PULLED OUT THE QRH AND FOLLOWED THE PROC; WHICH SAID TO RESET THE BLEED. THE FO WAS FLYING ON HIS WAY UP TO 17000 FT; OUR ASSIGNED ALT. UPON REACHING 17000 FT; BOTH BLEEDS FAILED. BLEED FAULT AND CLOSED LIGHTS ILLUMINATED WITH THE MASTER CAUTIONS. I RAN THE QRH PROCS WHICH LED ME TO DSND TO 10000 FT AND DEPRESSURIZE THE CABIN. I CALLED ATC AND REQUESTED A DSCNT TO 10000 FT AND TOLD THEM WE HAD A PRESSURIZATION PROB. ATC WAS VERY HELPFUL AND GAVE US IMMEDIATE CLRNC TO 10000 FT. THE FO WAS FLYING WITH THE AUTOPLT ON AND I INSTRUCTED HIM TO DSND TO 10000 FT IMMEDIATELY; WHICH HE DID. I WAS BUSY RUNNING THE QRH; BRIEFING THE FLT ATTENDANT ABOUT THE PROB; TALKING TO MAINT AND DISPATCH AS FUEL WOULD BE A CONCERN. I LOOKED AT THE ALT PASSING 13000 FT AND THE FO WAS FINE DSNDING DOWN TO 10000 FT. THE NEXT TIME I LOOKED OVER AT THE ALT WE WERE DSNDING THROUGH 9400 FT. I IMMEDIATELY SAID TO THE FO 'WHERE ARE YOU GOING?' HE IMMEDIATELY BEGAN A CLB BACK TO 10000 FT. DURING THE DSCNT WE WERE HANDED OFF TO ANOTHER ARTCC. ONCE WE WERE LEVEL AT 10000 FT; I CHKED IN WITH THE NEW CTLR. HE DID NOT SAY ANYTHING ABOUT OUR ALTDEV BUT WAS AWARE WE WERE HAVING PRESSURIZATION PROBS. WE CONTINUED THE FLT BACK TO ZZZ UNPRESSURIZED AT 10000 FT WITH NO FURTHER PROBS. THE EVENT OCCURRED BECAUSE I WAS IN A HIGH WORKLOAD SITUATION AND RELIED ON THE PF TO FLY THE AIRPLANE AND NOT BE DISTR BY WHAT I WAS DOING (TALKING TO ATC; FLT ATTENDANT; MAINT; AND DISPATCH) IN ADDITION TO RUNNING THE QRH. I BELIEVE HE BECAME DISTR BY MY ACTIONS AND WAS NOT PAYING ATTN TO THE ALT; ESPECIALLY SINCE THE ALT ALERTING SYS WAS DEFERRED. I BELIEVE THAT EVEN IN A HIGH WORKLOAD SITUATION HAD THE ALT ALERTING SYS BEEN WORKING WE WOULD NOT HAVE DSNDED BELOW OUR ASSIGNED ALT.