We show how to achieve large-amplitude oscillation and good frequency stability in a nonlinear NEMS oscillator by using a softening nonlinearity to locally balance the hardening behaviour of the Duffing nonlinearity for a given motion amplitude. The case when the softening behaviour is obtained via electrostatic biasing is theoretically investigated, under parallel-plate assumptions, for a fully-capacitive pulse-actuated resonant structure. This is validated by simulated data, in the case of a resonant clamped-clamped beam.