In recent years various authors have suggested that time dilation could solve the problem of seeing distant galaxies in a young universe. Time dilation which arises in both special and general relativity, could presumably slow earth clocks with respect to those on distant galaxies. This article examines how time dilation can arise within various relativistic cosmological models. It is found that in most cosmological models time dilation is either not significant or is in the wrong direction. Strong time dilation can occur in a static universe with pressure terms. However, in that case the predicted galactic red shifts would be much greater than those actually observed. It is concluded that the time dilation hypothesis thus faces a number of serious problems that must still be resolved.