Simple arguments are presented about critical-like phenomena associated with first-order phase transitions in systems described by non-conserved order parameters. A mean field theory gives a type of critical phenomena near the spinodal point, which is determined by a pseudo-free-energy and a Above the spinodal point, the problem is reduced to that of transient phenomena near the marginal case, whose time scale is prescribed by the imaginary part of the pseudo-order-parameter. Effects of fluctuations and possibilities of the observation are briefly discussed. From the linewidth measurement of light scattered by a binary liquid mixture, it has been observed that the diffusion coefficient D becomes smaller like D= (T-T 1 (c))r* when the temperature T approaches T 1 (c), where T 1 (c) represents the in the temperature-concentration (T-c) plane. v The pseudospinodal curve T 1 (c) is determined by the empirical form of D as extrapola tion. That is, the observations on stable homogeneous equilibrium states are ex trapolated into regions of the phase diagram in which the homogeneous states are unstable. Saito 2J has studied theoretically this problem, phenome na, by using the static renormalization-group method. 3J Since the homogeneous equilibrium states are unstable along T 1 (c), dynamical arguments will be necessary in connection with theoretical approaches. The above discussion concerns systems described by the conserved order param eter c. In such systems, there occurs the so-called spinodal decomposition!) On the other hand, in principle we may suppose that systems described by the non conserved order parameter s also show pseudo-critical phenomena. The spinodal represents generally the limits of stability of the metastable phase, and pseudo critical phenomena may occur in both systems with the conserved order parameter and those with the non-conserved order parameter. In the present paper, we discuss dynamics of pseudo-critical phenomena in systems described by the non-conserved order parameter. This is associated with first-order phase transitions, in which there exist metastable ordered states. It will be shown that behavior of dynamical quantities differs from that of the usual critical phenomena. Possibilities of their observation are also discussed later. Before considering the cases of the non-conserved order parameter, we first discuss, as an introduction, the cases of the conserved order parameter quoted in