Oscillation phase dynamics in the homogeneous autooscillating Belousov-Zhabotinsky (BZ) reaction have been studied by computer simulations. The wave dynamics in autooscillating media are qualitatively different from those in excitable media for sufficiently long waves. We propose a classification of chemical waves which is based on the analysis of the shape of the dispersion curve. This delimits conventionally the waves with properties analogous to those in excitable media, "trigger waves", from "phase waves". In particular, we study the phenomenon of the "dephasing wave", recently observed experimentally (Aliev, R. R. J. Phys. Chem. 1994, 98, 3999). This is a special form of phase wave dynamics, which looks like a propagating wave of phase triggering toward a uniform value. We show that phase wave dynamics, including the dephasing waves, can be described in terms of the phase diffusion equation, the well-known Burgers equation. This description remains qualitatively valid for a wide range of wavelengths.