POSSIBLE SYS ERROR AND POTENTIAL CONFLICT DURING A RWY INCURSION AS A TAXIING DC9-30; SEEMINGLY CLRED BY GND CTLR TO CROSS RWY 34; STOPS OVER THE HOLD SHORT LINE AFTER THE FLC NOTES A CESSNA CITATION ON SHORT FINAL TO RWY 34 AT HPN; NY.

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AFTER PUSHBACK FROM GATE AT HPN; THE BEFORE TAXI CHK WAS COMPLETED. THE FO CALLED FOR A TAXI CLRNC. THE RWY IN USE WAS RWY 34 AND TXWY A ON THE N SIDE OF RWY 34 WAS CLOSED. OUR INITIAL CLRNC WAS TO HOLD SHORT OF RWY 34 AT TXWY F. WE BEGAN A LOW PWR SLOW TAXI DUE TO HOLDING SHORT AND TERMINAL RAMP DIRECTLY BEHIND OUR ACFT. SHORTLY AFTER WE BEGAN OUR TAXI; HPN GND INSTRUCTED US (ACR X) TO FOLLOW A FALCON 50 JET; CROSS RWY 34; USE TXWY F AND TXWY L FOR FULL LENGTH RWY 34. WE CONTINUED OUR TAXI. REACHING THE RWY 34 HOLD LINE; I LOOKED AT THE RWY 34 APCH AREA. I DID NOT SEE ANY TFC SO WE PROCEEDED. APPROX 20 FT PAST THE HOLD LINE; THE FO AND MYSELF; LOOKING AT THE APCH END OF RWY 34; NOTED A CESSNA CITATION ON A SHORT FINAL. I SLAMMED ON THE BRAKES TO STOP SHORT OF RWY. THE FO NOTIFIED GND THAT WE WOULD HOLD SHORT. GND'S RESPONSE WAS 'ROGER' AS IF HE HAD NO IDEA THAT THERE WAS A POTENTIAL CONFLICT. SHORTLY AFTER THE CITATION WAS PAST TXWY F; GND CLRED US TO RESUME OUR TAXI TO RWY 34. THIS COULD HAVE BEEN DISASTROUS. MY SUGGESTION TO PREVENT FURTHER CONFUSION IN ADDITION TO THE PLTS CLRING THE RWY BEFORE XING: I THINK IF THE FAA REQUIRED ALL ACFT XING ACTIVE RWYS TO BE ON THE TWR FREQ AND BEING CTLED BY THE TWR; THIS WOULD GREATLY REDUCE CHANCE OF AN ERROR BY TAKING A GO-BTWN OUT OF THE PROCESS. ALSO; HAD THE GND CTLR ON DUTY INFORMED US OF THE TFC ON APCH; WE MAY NOT HAVE BEEN SURPRISED AT THE INTXN OF TXWY F AND RWY 34.