  We consider two fully frustrated Ising models: the antiferromagnetic
triangular model in a field of strength, $h=H T k_B$, as well as the Villain
model on the square lattice. After a quench from a disordered initial state to
T=0 we study the nonequilibrium dynamics of both models by Monte Carlo
simulations. In a finite system of linear size, $L$, we define and measure
sample dependent "first passage time", $t_r$, which is the number of Monte
Carlo steps until the energy is relaxed to the ground-state value. The
distribution of $t_r$, in particular its mean value, $< t_r(L) >$, is shown to
obey the scaling relation, $< t_r(L) > \sim L^2 \ln(L/L_0)$, for both models.
Scaling of the autocorrelation function of the antiferromagnetic triangular
model is shown to involve logarithmic corrections, both at H=0 and at the
field-induced Kosterlitz-Thouless transition, however the autocorrelation
exponent is found to be $H$ dependent.
