In Floer theory one has to deal with two-level manifolds like for instance the space of $W^{2,2}$ loops and the space of $W^{1,2}$ loops. Gradient flow lines in Floer theory are then trajectories in a two-level manifold. Inspired by our endeavor to find a general setup to construct Floer homology we therefore address in this paper the question if the space of paths on a two-level manifold has itself the structure of a Hilbert manifold. In view of the two topologies on a two-level manifold it is unclear how to define the exponential map on a general two-level manifold. We therefore study a different approach how to define charts on path spaces of two-level manifolds. To make this approach work we need an additional structure on a two-level manifold which we refer to as emph{tameness}. We introduce the notion of tame maps and show that the composition of tame is tame again. Therefore it makes sense to introduce the notion of a tame two-level manifold. The main result of this paper shows that the path spaces on tame two-level manifolds have the structure of a Hilbert manifold.