  For $\lambda$ an $n$-th power of a unit in a finite chain ring we prove that
$\lambda$-constacyclic repeated-root codes over some finite chain rings are
equivalent to cyclic codes. This allows us to simplify the structure of some
constacylic codes. We also study the $\alpha +p \beta$-constacyclic codes of
length $p^s$ over the Galois ring $GR(p^e,r)$.
