Algebraic structure of local symmetries for two-dimensional superparticles in a curved external background

Local symmetries structure for $(1,0)$- and $(1,1)$-superparticles in a curved external background is consistently studied. The minimal set of restrictions to be imposed on the background superfields for correct inclusion of interachtion is found from the requirement of correct number of first- and second-class constraints for the models. The most general form of local symmeries in this background is found. The resulting transformation contain contributions with torsion superfield. Gauge algebra is shown to be off-shell closed and nontrivially deformed as compared to the flat one. The requirement of the invariance of the action under direct generalization of the flat local symmetries is shown to lead to the full set of $d=2$ supergravity constraints.