In thin-film diffusion couples the sequential growth of equilibrium intermetallic compound phases and the missing of certain of them shown in the equilibrium phase diagram are well-known phenomena. It has been proposed that the first growing equilibrium phase has to exceed a critical thickness before a second equilibrium phase can start to grow. We investigate whether this concept can also be applied to the first growing phase which is a metastable amorphous alloy. We consider two different cases depending on the specific form of Gibbs' free energy-versus-composition diagrams. In the first case an analogous concept can be applied and the amorphous phase continues to grow after reaching its critical thickness. In the second case the amorphous phase starts to shrink after it has reached its critical thickness. For calculating the critical thickness in the second case a new procedure is suggested which is based on the maximum rate of decrease in Gibbs' free energy.