The dynamics of non-premixed edge-flames, including the generation of cellular Structures, in an unsteady, symmetric counterflow are examined for positive rates of strain. A one-step reaction is assumed, nu F-gamma + nu O-X -> nu P-p, in which the oxidizer Lewis number is 1. For a variety of Damkohler numbers, we examine the edge-flame evolution for two values of the fuel Lewis Dumber Le(gamma), 0.3 and 1, and two Values of the initial Mixture fraction gamma, 0.36 and 1, representing fuel lean and stoichiometric Supply conditions. For Le(gamma) = 0.3 and gamma = 0.36, unsteady forcing can convert non-cellular edge-flames into ones containing various characteristics of near- or sub-limit cellular Structures, including drifting, splitting and stationary flame strings. The transition regimes between the different edge-flame structures are examined as a function of the amplitude and frequency of the strain rate variations in the unsteady counterflow and also as a function of the instantaneous and equivalent strain rate functions. For Le(gamma) = 0.3 and gamma = 1, while no cellular edge-flames can be generated for steady counterflows, we show that cellular structures can be observed in the presence of unsteady forcing. For Le(gamma) = 1 and gamma = 1. it is shown that unsteady forcing can significantly modify the mean propagation speeds of both ignition and failure waves. Finally, the quenching boundaries of two-dimensional edge-flames induced by the unsteady counterflow are examined for Le(gamma) = 0.3, gamma = 0.36 and Le(gamma) = 1, gamma = 1. Published by Elsevier Inc. on behalf of The Combustion Institute.