  Nonequilibrium dynamics of the $\pm J$ Ising, the {\it XY}, and the
Heisenberg spin-glass models are investigated in three dimensions. A
nonequilibrium dynamic exponent is calculated from the dynamic correlation
length. The spin-glass dynamic exponent continuously depends on the
temperature. There is no anomaly at the critical temperature as is recently
reported by Katzgraber and Campbell. On the other hand, the chiral-glass
dynamic exponent takes a constant value above the spin-glass transition
temperature ($T_\mathrm{sg}$), and becomes temperature-dependent below
$T_\mathrm{sg}$.The finite-time scaling analyses on the spin- and the
chiral-glass susceptibility are performed using the temperature dependence of
the dynamic exponent. A difference of the spin- and the chiral-glass transition
temperatures is resolved in the Heisenberg model. The dynamic critical exponent
takes almost the same value for all transitions. It suggests that the
spin-glass and the chiral-glass transitions in three dimensions are dynamically
universal.
