We explore stability and instability of rapidly oscillating solutions x(t) for the hard spring delayed Duffing oscillatorFix T > 0. We target periodic solutions x n (t) of small minimal periods p n = 2T /n, for integer n → ∞, and with correspondingly large amplitudes. Simultaneously, for sufficiently large n ≥ n 0 , we obtain local exponential stability for (−1) n b < 0, and exponential instability for (−1) n b > 0, provided thatWe interpret our results in terms of noninvasive delayed feedback stabilization and destabilization of large amplitude rapidly periodic solutions in the standard Duffing oscillator. We conclude with numerical illustrations of our results for small and moderate n which also indicate a Neimark-Sacker-Sell torus bifurcation at the validity boundary of our theoretical results.