Flight Crew Air Transport Pilot (ATP)
ATC Issue All Types; Conflict NMAC
Flight Crew Took Evasive Action
Procedure
While on the MANSEC leg of the JFRYE3 STAR into ADS yesterday afternoon; we were issued a traffic call.  The ATC advisory informed traffic was at 1 to 2 O' Clock at 5;500 feet. We were on a heading of 090 and level at 6;000 feet as signed by ATC.  Upon visually scanning for traffic; which was also indicated on TCAS; I spotted the traffic at 1 to 1:30 and headed north; to cross our flight path right to left. The traffic looked to be closer in altitude than 500 feet; but at low altitudes it is often difficult to tell.  I informed the customer pilot in the right seat; who was working the radios that the traffic was in sight. He also confirmed a visual on the advisory target.  Approximately 10 seconds after the visual sighting a TCAS RA was issued to 'Monitor Vertical Speed'.  Within 5 seconds after that ATC issued a clearance to descend and maintain 3;000 feet. As that instruction was being issued an additional RA to 'Climb' was issued. Guidance was approximately 15 degrees nose up and traffic was indicated less than 300 feet below our aircraft.  I executed the RA instruction and informed ATC. ATC simply responded 'Okay; descend to 3;000 when able'. After receiving the 'Clear of Conflict' acknowledgment from the TCAS II system on the aircraft; the descent to 3;000 feet was initiated.
Corporate jet Captain reported a NMAC in the D10 TRACON area while on the JFRYE 3 arrival.