  We construct effective actions for non-Abelian 1/4
Bogomol'nyi-Prasad-Sommerfield (BPS) monopole-vortex complexes in 4d N = 2
supersymmetric gauge theories with gauge groups U(N), U(1) \times SO(2n) and
U(1) \times USp(2n). In the color-flavor locked vacuum with degenerate
hypermultiplet masses, a subgroup of the color-flavor diagonal symmetry remains
unbroken and gives internal orientational moduli to vortices which confine
monopoles in the Higgs phase. In this paper we discuss the effective action
which describes the interactions between monopoles and the orientational moduli
of non-Abelian vortices both from the bulk and vortex worldsheet theories. In
the large mass limit, we find that the effective action consists of
two-dimensional non-linear sigma models on vortex worldsheets and boundary
terms which describes monopole-vortex interactions.
