DNA methyltransferase 1 (Dnmt1) has a central role in copying the pattern of DNA methylation after replication which is one manifestation of epigenetic inheritance. With oligonculeotide substrates we show that mouse Dnmt1 has a 30- to 40-fold preference for hemimethylated DNA that is almost lost after addition of fully methylated oligonucleotides. Using long hemimethylated DNA substrates that carry defined methylation patterns and bisulfite analysis of the methylation reaction products, we show a 15-fold preference for hemimethylated CG sites. Dnmt1 moves along the DNA in a random walk methylating hemimethylated substrates with high processivity (>50 sites are visited on average which corresponds to linear diffusion over 6000 bp). The frequency of skipping sites is very low (<0.3%) and there is no detectable flanking sequence preference. CGCTC sites tend to terminate the processive methylation of DNA by Dnmt1. Unmethylated DNA is modified non-processively with a preference for methylation at CCGG sites. We simulate the propagation of methylation patterns using a stochastic model with the specificity of Dnmt1 observed here and conclude that either methylation of several sites is required to propagate the methylation information over several cellular generations or additional epigenetic information must be used.