  Phenomenological scaling arguments suggest the existence of universal
amplitudes in the finite-size scaling of certain correlation lengths in
strongly anisotropic or dynamical phase transitions. For equilibrium systems,
provided that translation invariance and hyperscaling are valid, the
Privman-Fisher scaling form of isotropic equilibrium phase transitions is
readily generalized. For non-equilibrium systems, universality is shown
analytically for directed percolation and is tested numerically in the
annihilation-coagulation model and in the pair contact process with diffusion.
In these models, for both periodic and free boundary conditions, the
universality of the finite-size scaling amplitude of the leading relaxation
time is checked. Amplitude universality reveals strong transient effects along
the active-inactive transition line in the pair contact process.
