Flight Crew Air Transport Pilot (ATP)
Other / Unknown
Conflict Airborne Conflict
Flight Crew Took Evasive Action
Human Factors; Airport; Airspace Structure
This was both the First Officer and Captain's first time to this airport. We had trouble picking up our clearance on the ground and were not familiar with procedures to get the clearance at the uncontrolled airport. We had to call on a phone to get the clearance and were given a 6 minute void time; which was extremely short. As we taxied out we talked to two aircraft on CTAF. One reported 10 miles out and inbound and another was taxiing behind us. The traffic that was in the pattern said that he had us in sight and said he would remain clear.  We took off and soon after our acceleration altitude we received a traffic alert from our TCAS. The traffic was approximately 2 to 5 miles in front of us and 400 feet above us. We both looked for the traffic but could not see him. We then received a RA command from TCAS to descend. We leveled off and started a descent. We then received another descend warning. I started a descent for a few hundred feet and then received an EGPWS warning to stop our decent. I leveled off as best I could to manage the two separate warnings to climb and descend. I am not sure how we could avoid this traffic conflict with out having a Controller or radar at the airport. We cleared the runway before taking it and we were talking to traffic in the pattern. We also checked TCAS before taking off.
SF340 Captain reports a TCAS RA to descend after flap retraction at an uncontrolled airport. The descend RA is repeated followed quickly by an EGPWS warning to; don't sink.