The reduction in scale of filamentary structures in stratospheric tracers due to stretching by the large-scale flow must ultimately be halted by processes that lead to molecular mixing. A quantitative bound on the strength of such processes, represented by an effective diffusivity D, is here inferred from high-resolution tracer data from recent airborne campaigns, using simple mathematical models representing the stretching and mixing processes. The mathematical models are based on the hypothesis that the filamentary structure observed along quasi-horizontal aircraft flight tracks corresponds in reality to the intersection of the flight track with sloping sheets of tracer. The aircraft data are analyzed to identify tracer features that unambiguously correspond to filamentary structures on isentropic surfaces. Clearly identifiable filaments are seen down to scales of less than 100 km, with transitions in tracer values at the edge of such filaments over scales of less than 10 km. Backward trajectories starting in the neighborhood of such filaments show convincingly that the air inside and outside the filaments has different origin. Integration of an equation for tracer gradient along forward trajectories allows the scale and orientation of the sloping tracer sheets corresponding to the observed filamentary structure to be deduced. On the assumption that the scale of the tracer sheets is small compared to the scale of variation of the velocity field, a diffusion equation may be derived that governs the spatial structure of the sheets. The diffusion coefficient in this equation is the product of the actual diffusivity D and a time-varying function that depends on the tracer gradient. The latter is determined by the forward integration along trajectories. The diffusion equation is integrated for different values of the diffusivity D. If the value of D is sufficiently large, the integration implies that the filament would diffuse away too rapidly to be consistent with the observations. Finding the maximum acceptable value of D gives an estimate of an upper bound on D for the real atmosphere. The results suggest that the value of D relevant to these filaments can be no more than 10-2 m2 s-1 and in some cases considerably less. Comparison is made with a recent analysis by Waugh et al., <1997>, who considered observed filaments that could, on the basis of the relation between mixing ratios of different tracers, be deduced to be partially mixed. Applying our method of analysis to the same observations suggests that the diffusivity D is about 1.4¿10-2 m2 s-1. This is consistent, if typical aspect ratios of horizontal to vertical scales are taken into account, with Waugh et al.'s estimate for an equivalent horizontal diffusivity.¿ 1997 American Geophysical Union