  We address the classification of ancient solutions to the Gauss curvature
flow under the assumption that the solutions are contained in a cylinder of
bounded cross section. For each cylinder of convex bounded cross-section, we
show that there are only two ancient solutions which are asymptotic to this
cylinder: the non-compact translating soliton and the compact oval solution
obtained by gluing two translating solitons approaching each other from time
$-\infty$ from two opposite ends.
