  We present an experimental and theoretical investigation of two-photon direct
frequency-comb spectroscopy performed through velocity-selective excitation. In
particular, we explore the effect of repetition rate on the
$\textrm{5S}_{1/2}\rightarrow \textrm{5D}_{3/2, 5/2}$ two-photon transitions
excited in a rubidium atomic vapor cell. The transitions occur via step-wise
excitation through the $\textrm{5P}_{1/2, 3/2}$ states by use of the direct
output of an optical frequency comb. Experiments were performed with two
different frequency combs, one with a repetition rate of $\approx 925$ MHz and
one with a repetition rate of $\approx 250$ MHz. The experimental spectra are
compared to each other and to a theoretical model.
