Can the type-IIB axion prevent Pre-Big Bang inflation?

We look at the possibility of superinflationary behavior in a class of anisotropic Type-IIB superstring cosmologies in the context of Pre-Big Bang scenario and find that there exists a rather narrow range of parameters for which these models inflate. We then show that, although in general this behavior is left untouched by the introduction of a Ramond-Ramond axion field through a SL(2,R) rotation, there exists a particular class of axions for which inflation disappears completely. Asymptotic past initial conditions are briefly discussed, and some speculations on the possible extension of Pre-Big Bang ideas to gravitational collapse are presented.