  We investigate uniform ergodic type theorems for additive and subadditive
functions on a subshift over a finite alphabet. We show that every strictly
ergodic subshift admits a uniform ergodic theorem for Banach-space-valued
additive functions. We then give a necessary and sufficient condition on a
minimal subshift to allow for a uniform subadditive ergodic theorem. This
provides in particular a sufficient condition for unique ergodicity.
