Actions for two-superparticle system in (10,2) dimensions and three-su
perparticle systems in (11,3) dimensions are constructed. These action
s have worldline bosonic and fermionic local symmetries, and target sp
ace global supersymmety generalizing the reparametrization, kappa-symm
etry and Poincare supersymmetry of the usual superparticle. With the s
econd particle, or the second and third particles on-shell, they descr
ibe a superparticle propagating in the background of a second superpar
ticle in (10,2) dimensions, or two other superparticles in (11,3) dime
nsions. Symmetries of the action are shown to exist in presence of sup
er Yang-Mills background as well. (C) 1997 Published by Elsevier Scien
ce B.V.