String and particle with two times

An action for a string and a particle with two timelike dimensions is proposed and analyzed. Because of the new gauge symmetries and associated constraints, the motion of each system in the background of the other is equivalent to the effective motion with a single timelike dimension. The quantum constraints are consistent only in critical dimensions. For the bosonic system in a 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.