We prove the existence of at least one T-periodic solution to a dynami
cal system of the type [GRAPHICS] where the potentials V(ij) are T-per
iodic in t and singular at the origin, u(i) is-an-element-of R(k), i =
1, ..., n, and k greater-than-or-equal-to 3. We also provide estimate
s on the H-1 norm of this solution. The proofs are based on a variant
of the Ljusternik-Schnirelman method. The results here generalize to t
he n-body problem some results obtained by BAHRI & RABINOWITZ on the 3
-body problem in [6].