We present field-theoretic and numerical studies of finite-size effect
s on the exponential relaxation times tau(1) and tau(2) of the order p
arameter and the square of the order parameter near the critical point
of three-dimensional Ising-like systems. Finite-size scaling function
s of tau(1) and tau(2) are calculated for the relaxational dynamics of
the phi(4) model in cubic geometry with periodic boundary conditions.
At T-c we predict the universal ratio tau(1)/tau(2) = 5.4. Below T-c,
a maximum of tau(2) is predicted. New Monte Carlo data for the Ising
model are presented which are in good agreement with the predictions.