Abstract : This thesis is concentrated on some probability and statistical issues linked to genomic comparison. In the first part we present a compound Poisson approximation for computing probabilities involved in significance tests for conserved genomic regions found by the reference-region approach. An important aspect of our computations is the fact that we are taking into account the existence of multigene families. In the second part we propose three measures, based on the transposition distance in the symmetric group, for quantifying the exceptionality of the gene order in conserved genomic regions. We obtain analytic expressions for their distribution in the case of a random permutation. In the third part of the thesis we study the distribution of the number of cycles in the breakpoint graph of a random signed permutation. We use the Markov chain imbedding technique to obtain this distribution in terms of a product of transition matrices of a certain finite Markov chain. The knowledge of this distribution provides a very good approximation for the distribution of the reversal distance.