The free energy of a vortex-antivortex pair in a Josephson-coupled lay
ered superconductor is derived within the framework of the Lawrence-Do
niach theory. We find that the free energy. of large pairs depends Lin
early on the pair separation and that there is no logarithmic term in
the free energy for large pairs. We also derive the free energy of a p
air of vortex lines, i.e., a vortex-antivortex pair in every layer. It
is found that the free energy of this system corresponds to the usual
result for conventional superconductors. In conclusion we discuss tha
t the vortex-antivortex interaction cannot be described by a simple mo
dification of the Kosterlitz-Thouless theory.