Distribution feedback semiconductor optical amplifiers (DFB-SOAs) have potential applications in optical signal processing because of lower switching-on threshold of bistability. By introducing spatial phase-shift and chirp, its bistable performance can be improved. If the amplifier operates at pulse state, signal transmission rate would be affected by the falling-edge distortion of output pulse and turn-on delay, so it is necessary to study its dynamic properties. In this paper, based on the coupled mode equation and carrier rate equation, the bistable dynamic characteristics of phased-shifted and chirped distributed-feedback semiconductor optical amplifiers have been investigated numerically. The results show that, the phase-shifted DFB-SOAs make the shape distortion of falling edge and turn-on delay of output pulse worsened firstly and then weakened with the decreased initial detuning, which can be suppressed by introducing chirp but being accompanied by the enhanced input peak overdrive.