  We compute the running of the spectrum of cosmological perturbations in
String Gas Cosmology, making use of a smooth parametrization of the transition
between the early Hagedorn phase and the later radiation phase. We find that
the running has the same sign as in simple models of single scalar field
inflation. Its magnitude is proportional to $(1 - n_s)$ ($n_s$ being the slope
index of the spectrum), and it is thus parametrically larger than for
inflationary cosmology, where it is proportional to $(1 - n_s)^2$.
