This paper is concerned with the stability of macroeconomic models in which there is no long-run trade-off between unemployment and inflation, because of a wage adjustment equation based on the NAIRU concept. It is shown, for a simple theoretical model and for the Bergstrom-Nowman-Wymer continuous-time macro-econometric model of the UK, that there is a bounded range of positive values of the wage acceleration parameter (determining the effect of labour demand on wage acceleration) for which the steady state is asymptotically stable. Then, each model generates damped cycles about a path converging to the steady-state neoclassical growth path.