We consider LieG-valued Yang-Mills fields on the space R×G/H, where G/H is a compact nearly Kähler six-dimensional homogeneous space, and the manifold R×G/H carries a G 2 -structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on R×G/H is reduced to Newtonian mechanics of a particle moving in R 6 , R 4 or R 2 under the influence of an inverted double-well-type potential for the cases G/H = SU(3)/U(1)×U(1), Sp(2)/Sp(1)×U (1) or G 2 /SU (3), respectively. We analyze all critical points and present analytical and numerical kink-and bounce-type solutions, which yield G-invariant instanton configurations on those cosets. Periodic solutions on S 1 ×G/H and dyons on iR×G/H are also given.

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