  The Josephson Effect provides a primary signature of single spin
superconductivity (SSS), the as yet unobserved superconducting state which was
proposed recently as a low temperature phase of half-metallic antiferromagnets.
These materials are insulating in the spin-down channel but are metallic in the
spin-up channel. The SSS state is characterized by a unique form of p-wave
pairing within a single spin channel. We develop the theory of a rich variety
of Josephson effects that arise due to the form of the SSS order parameter.
Tunneling is allowed at a SSS-SSS' junction but of course depends on the
relative orientation of their order parameters. No current flows between an SSS
and an s-wave BCS system due to their orthogonal symmetries, which potentially
can be used to distinguish SSS from other superconducting states. Single spin
superconductors also offer a means to probe other materials, where tunneling is
a litmus test for any form of ``triplet'' order parameter.
