A CE650 CAS aletered FUEL LOW PRESSURE LEFT AND RIGHT followed by FUEL BOOST LEFT AND RIGHT. The crew diverted to a nearby airport where the anomalies cleared. The crew refused to continue the trip with that aircraft.

Narrative

We were operating on a Part 135 flight. Approximately 20 minutes into the flight; we leveled off at 32;000 FT. I noticed a 260 LBS fuel imbalance and turned on cross feed to correct the imbalance. After approximately three minutes; the imbalance was zero so I turned off the cross feed. Immediately after turning off cross feed; we got an amber CAS message 'fuel low pressure left and right;' followed by an amber 'fuel boost on left and right.' We referred to the checklist; which directs you to match the boost pump condition and turn on the boost pump switches. After that; the CAS message turned cyan; which it is supposed to do. After discussing the situation; we both agreed the safe choice would be to find the nearest suitable airport. We both felt that with both engines showing a possible fuel pressure problem; it was best to get on the ground. We coordinated the diversion with ATC explaining the situation to them. We never declared an emergency; but requested quick handling. ATC was very helpful and got us to the nearby airport quickly. We were unable to inform the company of the diversion due to both the air phones being deferred and therefore inoperative. After landing and deplaning our passenger; I called Maintenance and did some troubleshooting with a controller and a representative from the CE-680 team. After several minutes; we were unable to duplicate it on the ground. We were then asked if we would like to continue flying the aircraft since we were unable to duplicate the issue. Both my partner and I decided that wasn't a good idea and elected to send in the write up.