We consider LieG-valued Yang-Mills fields on the space RxG/H, where G/H is a compact nearly Kahler six-dimensional homogeneous space, and the manifold RxG/H carries a G(2)-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on RxG/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)xU(1), Sp(2)/Sp(1)xU(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)xG/H and dyons on iRxG/H are also given.