The critical dynamics of the time-dependent Ginzburg-Landau model for a system with quenched random impurities and nonconserved order parameter is studied in the framework of the $\ensuremath{\epsilon}$ expansion. In contrast to the situation in pure systems, the dynamic critical exponent
z deviates from its conventional value at first order in $\ensuremath{\epsilon}\ensuremath{\equiv}4\ensuremath{-}d$. The impurities cause an enhancement of the shape function ${f}_{x}(\ensuremath{\nu})$ at small frequencies $\ensuremath{\nu}$; ${f}_{x}(\ensuremath{\nu}=0)$ diverges as $T\ensuremath{\rightarrow}{T}_{c}$. Below
Tc the equation of state, static susceptibility $\ensuremath{\chi}$, and dynamic response function
G, are studied. A new, purely static correlated function,
C(s), whose existence is unique to the random system is introduced. The coexistence curve singularities of
C(s), $\ensuremath{\chi}$, and
G in systems with continuously broken symmetry are explored. The connection of the quenched-impurity model with "model
C" of Halperin, Hohenberg, and Ma is discussed.
Effects of quenched random magnetic fields on the critical relaxation of the time-dependent Ginzburg-Landau equation for m-component classical spin system are investigated by means of the dynamical renormalization group. In the static limit, the recursion relations near below 6 space dimensions found by Grinstein are recovered. Dynamic critical exponent for the characteristic frequency is obtained to be z = 2 + c η, c = 2 up to order ε2 (ε= 6 - d) on the basis of the dynamic scaling hypothesis. The static correlation exponent η is given by that of a pure system in d - 2 space dimensions. Since c does not agree with the result by Halperin-Hohenberg-Ma (c = 6 log (4/3) - 1), d →d - 2 rule does not hold for time-dependent phenomena.