The talk will have two parts. First, a general, introductory-level survey of the work by Belinskii, Khalatnikov and Lifshitz (BKL) on the generic behaviour of the gravitational field in the vicinity of a spacelike (cosmological) singularity will be given. Second, recent
extensions of these ideas to superstring cosmology will be discussed. It will be shown that the general solution near a spacelike singularity of the Einstein-dilaton-p-form field equations relevant to superstring theories and M-theory exhibits an oscillatory behaviour of the chaotic, BKL type.