In this talk I present a recent result (in collaboration with Todd Oliynyk from Monash) about the asymptotic dynamics of perfect fluids with linear equations of state near Kasner and Kasner-scalar field big bang singularities. This is a nonlinear stability result under the condition that the speed of sound of the fluid satisfies a lower bound determined by the Kasner exponents. In addition I provide evidence that this lower bound is sharp.