  We obtain BPS Z(2) monopole solutions in Yang-Mills-Higgs theories with the
gauge group SU(n) broken to Spin(n)/Z(2) by a scalar field in the nxn
representation. We show that the magnetic weights of the so-called fundamental
Z(2) monopoles correspond to the weights of the defining representation of the
algebra dual to so(n), and the masses of the nonfundamental BPS Z(2) monopoles
are equal to the sum of the masses of the constituent fundamental monopoles. We
also show that the vacua responsible for the existence of these Z(2) monopoles
are present in the Higgs branch of a class of N=2 SU(n) superconformal field
theories. We analyze some dualities these monopoles may satisfy.
