  We consider a vectorial, confining SU(N) gauge theory with a variable number,
$N_f$, of massless fermions transforming according to the fundamental
representation. Using the Schwinger-Dyson and Bethe-Salpeter equations, we
calculate the $S$ parameter in terms of the current-current correlation
functions. We focus on values of $N_f$ such that the theory is in the crossover
region between the regimes of walking behavior and QCD-like (non-walking)
behavior. Our calculations indicate that the contribution to $S$ from a given
fermion decreases as one moves from the QCD-like to the walking regimes. The
implications of this result for technicolor theories are discussed.
