We analyze the front structures evolving under the difference-differential equation ∂tCj =
−Cj+C2j−1
from initial conditions 0 [les ] Cj(0) [les ] 1 such that Cj(0) → 1 as j → ∞ suffciently
fast. We show that the velocity v(t) of the front converges to a constant value v* according to
v(t) = v*−3/(2λ*t)+(3√π/2) Dλ*/(λ*2Dt)3/2+[Oscr ](1/t2). Here v*, λ* and D are determined by
the properties of the equation linearized around Cj = 1. The same asymptotic expression is
valid for fronts in the nonlinear diffusion equation, where the values of the parameters λ*, v*
and D are specific to the equation. The identity of methods and results for both equations is
due to a common propagation mechanism of these so-called pulled fronts. This gives reasons
to believe that this universal algebraic convergence actually occurs in an even larger class of
equations.