  We study a class of planar billiards having the remarkable property that
their phase space consists up to a set of zero measure of two invariant sets
formed by orbits moving in opposite directions. The tables of these billiards
are tubular neighborhoods of differentiable Jordan curves that are unions of
finitely many segments and arcs of circles. We prove that under proper
conditions on the segments and the arcs, the billiards considered have non-zero
Lyapunov exponents almost everywhere. These results are then extended to a
similar class of of 3-dimensional billiards. Finally, we find that for some
subclasses of track billiards, the mechanism generating hyperbolicity is not
the defocusing one that requires every infinitesimal beam of parallel rays to
defocus after every reflection off of the focusing boundary.
