In this paper we present some theoretical results on two forms of multi-point crossver: n-point crossover and uniform crossover. This analysis extends the work from De Jong's thesis, which dealt with disruption of n-point crossover on 2nd order hyperplanes. We present various extensions to this theory, including 1) an analysis of the disruption of n-point crossover on kth order hyperplanes; 2) the computation of tighter bounds on the disruption caused by n-point crossover, by handling cases where parents share critical allele values; and 3) an analisys of the disruption caused by uniform crossover on kth order hyperplanes. The implications of these results on implementation issues and performance are discussed, and several directions for further research are suggested.