  It is proposed the generalized action functional for N=1 superparticle in
D=3,4,6 and 10 space-time dimensions. The superfield geometric approach
equations describing superparticle motion in terms of extrinsic geometry of the
worldline superspace are obtained on the base of the generalized action. The
off-shell superdiffeomorphism invariance (in the rheonomic sense) of the
superparticle generalized action is proved. It was demonstrated that the half
of the fermionic and one bosonic (super)fields disappear from the generalized
action in the analytical basis. Superparticle interaction with Abelian gauge
theory is considered in the framework of this formulation. The geometric
approach equations describing superparticle motion in Abelian background are
obtained.
