We look at the possibility of superinflationary behavior in a class ofanisotropic Type-IIB superstring cosmologies in the context of Pre-big Bangscenario and find that there exists a rather narrow range of parameters forwhich these models inflate. We then show that, although in general thisbehavior is left untouched by the introduction of a Ramond-Ramond axion fieldthrough a SL(2,R) rotation, there exists a particular class of axions for whichinflation disappears completely. Asymptotic past initial conditions are brieflydiscussed, and some speculations on the possible extension of Pre-big Bangideas to gravitational collapse are presented.
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