  We study the behaviour of spherical Voids in Lagrangian perturbation theories
L(n), of which the Zel'dovich approximation is the lowest order solution L(1).
We find that at early times higher order L(n) give an increasingly accurate
picture of Void expansion. However at late times particle trajectories in L(2)
begin to turnaround and converge leading to the {\em contraction} of a Void, a
sign of pathological behaviour. By contrast particle trajectories in L(3) are
well behaved and this approximation gives results in excellent agreement with
the exact top-hat solution as long as the Void is not too underdense. For very
underdense Voids, L(3) evacuates the Void much too rapidly leading us to
conclude that the Zel'dovich approximation L(1), remains the best approximation
to apply to the late time study of Voids. The behavior of high order
approximations in spherical voids is typical for asymptotic series and may be
generic for Lagrangian perturbation theory.
