According to the recent lattice QCD results and the model calculations, the critical end point is expected to exist in the QCD phase diagram in the plane of temperature and baryon chemical potential. In these calculations, however, studied primarily are the static properties of the critical point from the viewpoint of chiral symmetry. Here we investigate the dynamical aspect of the soft mode accompanied by the critical end point within two chiral effective models, the Nambu-Jona-Lasinio model and the linear sigma model with quarks. The dynamical aspect at the critical point is of interest in itself, and furthermore it will become more important when its implications are considered in the context of heavy ion physics. It will be shown that the relevant soft mode is the collective fluctuation of the particle distribution with spacelike dispersion, whereas the sigma mode, which is the chiral partner of the pion, remains massive at the critical point in these models. It seems natural because this critical point is similar to the liquid-gas critical point, rather than the chiral one. The soft mode is formed of the scalar, vector, and energy density fluctuations. The chiral and tri-critical transition points will be also discussed for comparison and completeness.