  For the cylindrically symmetric ''asymptotically flat'' Einstein equations in
the case of electro-vacuum it is known that solutions exist globally and also
that this class of spacetimes is causally geodesically complete. Hence strong
cosmic censorship holds for this class. An interesting question is whether
these results can be generalized to include spacetimes with phenomenological
matter, e.g. collisionless matter described by the Vlasov equation. Spherically
symmetric asymptotically flat solutions of the Einstein-Vlasov system with
small initial data are known to be causally geodesically complete. For
arbitrary (in size) data it has been shown that if a singularity occurs, the
first one occurs at the center of symmetry. In this paper we begin to study the
question of global existence for the cylindrically symmetric Einstein-Vlasov
system with general (in size) data and we show that if a singularity occurs at
all, the first one occurs at the axis of symmetry.
