An n-quasigroup (Q,f) is called dihedral iff f(xi,...,x„) = xn+1 o *<,(„)) = *<,(„+i) for every permutation a £ Dn+U where Dn+1 is the dihedral subgroup of the symmetric group S„+1 of degree n + 1 . Dihedral n-quasigroups (D-n-quasigroups) represent a generalization of totally symmetric binary quasigroups. In the paper several classes of D-n-quasigroups are considered: (ij)-associative D-n-quasigroups, D-n-groups, medial D-n-quasigroups, self-orthogonal D-n-quasigroups and D-n-quasigroups satisfying Menger identities. Their properties are described and some characterizations given.