Spatio-temporal instability of the fundamental mode in Yb(3+)-doped few-mode PM fiber amplifiers with a core diameter of 8.5 μm was registered at 2-30 Watts pump power. Both experimental and theoretical analysis revealed the nonlinear power transformation of the LP(01) fundamental mode into high-order modes. Numerical simulation revealed self-consistent growth of the higher-order mode and traveling electronic index grating accompanying the population grating induced by the mode interference field (due to different polarizability of the excited and unexcited Yb(3+) ions). Experimental results and numerical calculations showed the increase of the instability threshold along with an increase of the signal frequency bandwidth.