  We consider an autonomous system in R^n having a limit cycle x_0 of period
T>0 which is nondegenerate in a suitable sense. We then consider the perturbed
system obtained by adding to the autonomous system a T-periodic, not
necessarily differentiable, term whose amplitude tends to 0 as a small
parameter e>0 tends to 0. Assuming the existence of a T-periodic solution x_e
of the perturbed system and its convergence to x_0 as e->0, the paper
establishes the existence of d_e->0 as e->0 such that \|x_e(t+d_e)-x_0(t)\|<=eM
for some M>0 and any e>0 sufficiently small.
