The asymptotic behaviour of the iterative proportional fitting procedure (IPF procedure) is analysed comprehensively. Given a nonnegative matrix as well as row and column marginals the IPF procedure generates a sequence of matrices, called the IPF sequence, by alternately fitting rows and columns to match their respective marginals. We prove that the IPF sequence has at most two accumulation points. They originate as the limits of the even-step subsequence, and of the odd-step subsequence. The well-known IPF convergence criteria are then retrieved easily. Our proof is based on Csiszár TMs and TusnádyTMs (1984) results on the interplay of I-divergence geometry and alternating minimisation procedures. Moreover, a characterisation of the two accumulation points by means of I-divergence is given as well as an outlook on the asymptotic nalysis of the multivariate IPF procedure used to fit contingency tables to given marginals. (joint work with Fabian Reffel)