Detailed simulations are performed for a series of steady and unsteady nonpremixed flames. A specific type of unsteady flamelet simulations are considered, i.e., flamelets subjected to (temporally) varying strain-rates. It is observed that the unsteady flame trajectories move closely along a 2D manifold describing the set of stead), diffusion flames in composition space. Using the 2D manifold, unsteady simulations are performed. It is shown that there is a phase shift in the species mass fractions between the detailed simulations and the 2D FGM simulations. This phase shift can be avoided when an additional controlling variable is used. Using unsteady flamelet Simulations, a 3D manifold is generated, which is parameterized using three controlling variables. Furthermore, this 3D FGM accurately predicts a broad range of the strain-rate parameters: the mean strain-rate, the applied amplitude, and the frequency of the sinusoidally varying strain-rate. Finally, it is shown that the aforementioned phase shift between the detailed simulations and the 3D FGM simulations disappears. (c) 2008 The Combustion Institute. Published by Elsevier Inc. All rights reserved.