  An action for a string and a particle with two timelike dimensions is
proposed and analyzed. Due to new gauge symmetries and associated constraints,
the motion of each system in the background of the other is equivalent to
effective motion with a single timelike dimension. The quantum constraints are
consistent only in critical dimensions. For the bosonic system in flat
spacetime the critical dimension is 27 or 28, with signature (25,2) or (26,2),
depending on whether the particle is massive or massless respectively. For the
supersymmetric case the critical dimensions are 11 or 12, with signature (9,2)
or (10,2), under the same circumstances. Generalizations to multiparticles,
strings and p-branes are outlined.
