We study topological as well as dynamical properties of BPS nonabelian magnetic monopoles of Goddard-Nuyts-Olive-Weinberg type in $ G=SU(N)$, $USp(2N)$ and SO(N) gauge theories, spontaneously broken to nonabelian subgroups $H$. We find that monopoles transform under the group dual to $H$ in a tensor representation of rank determined by the corresponding element in $\pi_1(H)$. When the system is embedded in a $\cal N=2$ supersymmetric theory with an appropriate set of flavors with appropriate bare masses, the BPS monopoles constructed semiclassically persist in the full quantum theory. This result supports the identification of "dual quarks'' found at $r$-vacua of $\cal N=2$ theories with the nonabelian magnetic monopoles. We present several consistency checks of our monopole spectra.