The non-premixed edge flame stabilized downstream of a splitter plate separating co-flowing streams of fuel and oxidizer exhibits thermal-diffusive instability for Lewis numbers of the reactants (taken as equal) greater than unity. This paper reports external excitation of a flame exhibiting such instability at imposed frequencies that are factors or multiples of the natural frequency. A two-dimensional unsteady framework is adopted, and the problem is solved numerically. First, the regimes of Damköhler and Lewis numbers for steady flame versus an intrinsically oscillating flame are explored. The natural frequency of oscillations increases with increase in the Damköhler number, but their amplitudes decrease. Two cases, both at a constant Lewis number of 1.7, are considered, one at a high Damköhler number where the unexcited flame is steady, and another at a low Damköhler number where it exhibits intrinsic instability. The amplitude of the external excitation is varied. It is found that, while the steady flame responds predominantly at the external excitation frequency as expected, the oscillating flame exhibits this behaviour only for excitation frequencies ≤ the natural frequency, over a range that expands with increase in the excitation amplitude. For excitation frequencies higher than the natural frequency, the flame responds predominantly at the natural frequency. This shows that the thermal-diffusive instability mechanism is rate-limiting for external oscillation time-scales smaller than its characteristic time-scale. © 2007 Combustion Institute. All Rights Reserved.