This paper reports numerical investigations on the effects of flowfield unsteadiness on the structure and extinction of strained laminar non-premixed flames. The unsteady conservation equations of mass, momentum, energy and species were solved along the stagnation streamline of an opposed jet counterflow within a finite domain, including detailed descriptions of the chemistry and molecular transport. The unsteadiness was introduced by imposing sinusoidal variations of the reactant velocity, concentration, and temperature at the exit of the nozzles. The results demonstrate that at low frequencies the flame structure reacts to the imposed oscillations in a quasi-steady manner, while, at high frequencies, transient effects that result in reduced flame response must be accounted for. It was also found that even though the flame response is diminished at high frequencies, there is still a substantial transient effect felt far from the flame at the interface between the hydrodynamic and the main diffusive zones that appears to accumulate mass and distort the fluid mechanics before the flame zone. These phenomena were physically explained from first principles. The effect of unsteadiness on extinction was also assessed, and the phenomena of partial extinction and re-ignition, extinction delay and extinction suppression were identified. Detailed analysis showed that these phenomena are being controlled by the relative magnitudes of the time scales of the imposed oscillations and the time required for permanent extinction. The results of this analysis are of particular importance to the formulation of laminar flamelet libraries that are needed for the realistic modelling of large-scale combustion devices. Copyright (C) 2000 John Wiley & Sons, Ltd.