B757-200
Flight Crew Air Transport Pilot (ATP)
Deviation - Altitude Excursion From Assigned Altitude
Air Traffic Control Issued Advisory / Alert; Flight Crew Took Evasive Action
Airspace Structure; Aircraft
As we leveled at 8;000 feet approaching LUVLY; the TCAS RA commanded a climb to avoid a rapidly ascending aircraft.  We complied with the RA and climbed to 8;250 feet for approximately 10 seconds.  We informed approach that we were complying with an RA.  We subsequently returned to 8;000 feet.
On FLIPR arrival into MIA level at 8;000 FT; ATC called traffic climbing out of MIA to 7;000 FT.  TCAS issued an RA for a gentle climb.  We complied with the TCAS RA; notified ATC and climbed to about 8;250 FT.  Upon TCAS 'Clear of conflict' message; we returned to the assigned altitude.  Aircraft on climb out leveled at 7;000 FT as expected and at no time was there a loss of separation or was safety compromised.If the aircraft on departure that are being vectored under the arrival aircraft have a sufficiently [high] rate of climb; then TCAS will issue an alert or a resolution based on the rate of climb.  Aircrews should be advised that reducing the rate of climb to 1;000 FPM or less during the last 1;000 FT of the climb out will prevent this from occurring.
Flight Crew describes a TCAS RA event while arriving into MIA caused by the climb rate of a departing aircraft leveling 1;000 feet below.  The reporters aircraft climbed 250 feet to comply with the RA then returned to 8;000 feet.