This paper investigates the conditions under which flame pinch-off occurs in forced and non-forced, buoyant laminar jet diffusion flames. The fuel jet emerges into a stagnant air atmosphere at temperature T(0), with a velocity that varies periodically in time with non-dimensional frequency omega(t) and amplitude A = 0.5. We use the formulation developed by Linan and Williams [1] based on the combination of the mass fraction and energy conservation equations to eliminate the reaction terms, that are substituted by the mixture fraction Z and the excess-enthalpy H scalar conservations equations. With this formulation, valid for arbitrary Lewis numbers, the flame lies on the stoichiometric mixture fraction level surface Z = Z(s) and its temperature can be easily calculated as T(e)'/T(0) = 1 + gamma(1 + H(s)), where Z(s) = 1/(1 + S), gamma is the non-dimensional heat release parameter, S is the air needed to burn the unit mass of fuel and H(s) is the value of the excess enthalpy at the flame surface. Non-modulated flames omega(t) = 0 subjected to a gravity field g are known to flicker at a non-dimensional frequency omega(t,0) that depends on the Froude number Fr(l). The surface of the flame is deformed by the buoyancy-induced oscillations and, for Froude numbers below a certain critical value Fr(lc) the flame breaks repeatedly in two different combustion regions (pinch-off). The first one remains attached to the burner and constitutes the main flame. The second region detaches from the tip of the flame, forming a pocket of hot gas surrounded by a flame that travels along the downstream coordinate z with velocity (u) over bar similar to (gamma z/Fr(l)(2))(1/2) until the fuel inside the pocket is depleted. Pinch-off is affected by the modulation of the velocity of the jet, changing the critical Froude number of pinch-off Fr(l,c) as the excitation frequency omega(t) is modified. Very large omega(t)/omega(l,0) >> 1 or very small omega(t)/omega(l,0) << 1 excitation frequencies do not modify Fr(l,c) and it remains equal to Fr(l,c)(infinity). For omega(t)/omega(l,0) similar to O(1), the response of the flame is determined by the ratio l/x(g) = gamma/Fr(l), where I represents the flame length and x(g) is the distance at which buoyancy effects become important. A strong resonance is observed at w(t) similar to omega(t,0) if the flame is sufficiently long, giving Fr(t,c) that could be thirty times larger than Fr(t,c)(infinity). Short flames dc not present that peak and Fr(l,c) remains almost independent of omega(l). (C) 2011 The Combustion Institute. Published by Elsevier Inc. All rights reserved.