Let G be a semisimple complex Lie group with a Borel subgroup B. Let X=G/B be the flag manifold of G. Let C=\PP1 ' ¥Unknown control sequence '\PP' be the projective line. Let a Î H2(\bX,\Bbb Z)Unknown control sequence '\bX'. The moduli space of G-monopoles of topological charge f is naturally identified with the space \CMb(\bX,a)Unknown control sequence '\CM' of based maps from (C,X) to (X,B) of degree f. The moduli space of G-monopoles carries a natural hyperkähler structure, and hence a holomorphic symplectic structure. It was explicitly computed by R. Bielawski in case G=SLn. We propose a simple explicit formula for another natural symplectic structure on \CMb(\bX,a)Unknown control sequence '\CM' . It is tantalizingly similar to R. Bielawski's formula, but in general (rank >1) the two structures do not coincide. Let P´G be a parabolic subgroup. The construction of the Poisson structure on \CMb(\bX,a)Unknown control sequence '\CM' generalizes verbatim to the space of based maps \CM = \CMb(\bG/\bP,b)Unknown control sequence '\CM'. In most cases the corresponding map T*\CM® T\CMUnknown control sequence '\CM' is not an isomorphism, i.e. \CMUnknown control sequence '\CM' splits into nontrivial symplectic leaves. These leaves are explicilty described.