Superstrings with new supersymmetry in (9,2) and (10,2) dimensions

We construct superstring theories that obey the new supersymmetry algebra $\{Q_{\alpha }{,Q}_{\beta }\}={\gamma }_{\alpha \beta }^{\mu \nu }{P}_{1\mu }{P}_{2\nu }$ in a Green-Schwarz formalism, with kappa supersymmetry also of the new type. The superstring is in a system with a superparticle so that their total momenta are $P_{2\mu }{,P}_{1\nu },$ respectively. The system is covariant and critical in (10,2) dimensions if the particle is massless and in (9,2) dimensions if the particle is massive. Both the superstring and superparticle have coordinates with two timelike dimensions but each behaves effectively as if they have a single timelike dimension. This is due to gauge symmetries and associated constraints. We show how to generalize the gauge principle to more intricate systems containing two parts, 1 and 2. Each part contains interacting constituents, such as $p$-branes, and each part behaves effectively as if they have one timelike coordinate, although the full system has two timelike coordinates. The examples of two superparticles, and of a superparticle and a superstring, discussed in more detail are special cases of such a generalized interacting system.