The dynamics of phase separation in two-dimensional binary fluid with low-middle densities was investigated by molecular dynamics simulation. The spinodal decomposition region for symmetric systems may be divided into the diffusive and kinematic region. At an elevated temperature, the motion of particles is diffusive. At a middle temperature, the kinematic mechanism takes effect on the systems with middle density, and the diffusive mechanism holds only for the dilute system. At a low temperature, the phase separation obeys the kinematic mechanism in a wide range of density. For asymmetric systems, the growth of particles A (majority) is different from that of particles B (minority). The diffusive and kinematic regions for the majority are similar to those of symmetric system. The growth exponent for the minority is related to its absolute density and temperature because of its small density.