The algebraic structures in term of polynomial generators of all constacyclic codes of length 2ps over the finite field Fpm are established. Among other results, all self-dual negacyclic codes of length 2ps, where p ≡ 1 (mod 4) (any m), or p ≡ 3 (mod 4) and m is even, are provided. It is also shown the non-existence of self-dual negacyclic codes of length 2ps, where p ≡ 3 (mod 4), m is odd, and self-dual cyclic codes of length 2ps, for any odd prime p.