  We investigate the structure of locally finite profinite rings. We classify
(Jacobson-) semisimple locally finite profinite rings as products of complete
matrix rings of bounded cardinality over finite fields, and we prove that the
Jacobson radical of any locally finite profinite ring is nil of finite
nilexponent. Our results apply to the context of small compact $G$-rings, where
we also obtain a description of possible actions of $G$ on the underlying ring.
